Addendum: A graph placement methodology for fast chip design

<!DOCTYPE html> <html lang="en" class="grade-c"> <head> <title>Addendum: A graph placement methodology for fast chip design | Nature</title> <link rel="alternate" type="application/rss+xml" href="https://www.nature.com/nature.rss"/> <script id="save-data-connection-testing"> function hasConnection() { return navigator.connection || navigator.mozConnection || navigator.webkitConnection || navigator.msConnection; } function createLink(src) { var preloadLink = document.createElement("link"); preloadLink.rel = "preload"; preloadLink.href = src; preloadLink.as = "font"; preloadLink.type = "font/woff2"; preloadLink.crossOrigin = ""; document.head.insertBefore(preloadLink, document.head.firstChild); } var connectionDetail = { saveDataEnabled: false, slowConnection: false }; var connection = hasConnection(); if (connection) { connectionDetail.saveDataEnabled = connection.saveData; if (/\slow-2g|2g/.test(connection.effectiveType)) { connectionDetail.slowConnection = true; } } if (!(connectionDetail.saveDataEnabled || connectionDetail.slowConnection)) { createLink("/static/fonts/HardingText-Regular-Web-cecd90984f.woff2"); } else { document.documentElement.classList.add('save-data'); } </script> <link rel="preconnect" href="https://cmp.nature.com" crossorigin> <meta http-equiv="X-UA-Compatible" content="IE=edge"> <meta name="applicable-device" content="pc,mobile"> <meta name="viewport" content="width=device-width,initial-scale=1.0,maximum-scale=5,user-scalable=yes"> <meta name="360-site-verification" content="5a2dc4ab3fcb9b0393241ffbbb490480" /> <script data-test="dataLayer"> window.dataLayer = [{"content":{"category":{"contentType":"addendum","legacy":{"webtrendsPrimaryArticleType":"amendments and corrections","webtrendsSubjectTerms":"computational-science;electrical-and-electronic-engineering","webtrendsContentCategory":null,"webtrendsContentCollection":null,"webtrendsContentGroup":"Nature","webtrendsContentGroupType":null,"webtrendsContentSubGroup":"Addendum","status":null}},"article":{"doi":"10.1038/s41586-024-08032-5"},"attributes":{"cms":null,"deliveryPlatform":"oscar","copyright":{"open":false,"legacy":{"webtrendsLicenceType":null}}},"contentInfo":{"authors":["Anna Goldie","Azalia Mirhoseini","Mustafa Yazgan","Joe Wenjie Jiang","Ebrahim Songhori","Shen Wang","Young-Joon Lee","Eric Johnson","Omkar Pathak","Azade Nova","Jiwoo Pak","Andy Tong","Kavya Srinivasa","William Hang","Emre Tuncer","Quoc V. Le","James Laudon","Richard Ho","Roger Carpenter","Jeff Dean"],"publishedAt":1727308800,"publishedAtString":"2024-09-26","title":"Addendum: A graph placement methodology for fast chip design","legacy":null,"publishedAtTime":null,"documentType":"aplusplus","subjects":"Computational science,Electrical and electronic engineering"},"journal":{"pcode":"nature","title":"nature","volume":"634","issue":"8034","id":41586,"publishingModel":"Hybrid Access"},"authorization":{"status":true},"features":[{"name":"furtherReadingSection","present":true}],"collection":null},"page":{"category":{"pageType":"article"},"attributes":{"template":"mosaic","featureFlags":[{"name":"nature-onwards-journey","active":false}],"testGroup":null},"search":null},"privacy":{},"version":"1.0.0","product":null,"session":null,"user":null,"backHalfContent":true,"country":"HK","hasBody":true,"uneditedManuscript":false,"twitterId":["o3xnx","o43y9","o3ef7"],"baiduId":"d38bce82bcb44717ccc29a90c4b781ea","japan":false}]; window.dataLayer.push({ ga4MeasurementId: 'G-ERRNTNZ807', ga360TrackingId: 'UA-71668177-1', twitterId: ['3xnx', 'o43y9', 'o3ef7'], baiduId: 'd38bce82bcb44717ccc29a90c4b781ea', ga4ServerUrl: 'https://collect.nature.com', imprint: 'nature' }); </script> <script> (function(w, d) { w.config = w.config || {}; w.config.mustardcut = false; if (w.matchMedia && w.matchMedia('only print, only all and (prefers-color-scheme: no-preference), only all and (prefers-color-scheme: light), only all and (prefers-color-scheme: dark)').matches) { w.config.mustardcut = true; d.classList.add('js'); d.classList.remove('grade-c'); d.classList.remove('no-js'); } })(window, document.documentElement); </script> <style>@media only print, only all and (prefers-color-scheme: no-preference), only all and (prefers-color-scheme: light), only all and (prefers-color-scheme: dark) { .c-article-editorial-summary__container .c-article-editorial-summary__article-title,.c-card--major .c-card__title,.c-card__title,.u-h2,.u-h3,h2,h3{-webkit-font-smoothing:antialiased;font-family:Harding,Palatino,serif;font-weight:700;letter-spacing:-.0117156rem}.c-article-editorial-summary__container .c-article-editorial-summary__article-title,.c-card__title,.u-h3,h3{font-size:1.25rem;line-height:1.4rem}.c-reading-companion__figure-title,.u-h4,h4{-webkit-font-smoothing:antialiased;font-weight:700;line-height:1.4rem}html{text-size-adjust:100%;box-sizing:border-box;font-size:100%;height:100%;line-height:1.15;overflow-y:scroll}body{background:#eee;color:#222;font-family:-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Oxygen-Sans,Ubuntu,Cantarell,Helvetica Neue,sans-serif;font-size:1.125rem;line-height:1.76;margin:0;min-height:100%}details,main{display:block}h1{font-size:2em;margin:.67em 0}a,sup{vertical-align:baseline}a{background-color:transparent;color:#069;overflow-wrap:break-word;text-decoration:underline;text-decoration-skip-ink:auto;word-break:break-word}b{font-weight:bolder}sup{font-size:75%;line-height:0;position:relative;top:-.5em}img{border:0;height:auto;max-width:100%;vertical-align:middle}button,input,select{font-family:inherit;font-size:100%;line-height:1.15;margin:0}button,input{overflow:visible}button,select{text-transform:none}[type=submit],button{-webkit-appearance:button}[type=checkbox]{box-sizing:border-box;padding:0}summary{display:list-item}[hidden]{display:none}button{border-radius:0;cursor:pointer;font-family:-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Oxygen-Sans,Ubuntu,Cantarell,Helvetica Neue,sans-serif}h1{-webkit-font-smoothing:antialiased;font-family:Harding,Palatino,serif;font-size:2rem;font-weight:700;letter-spacing:-.0390625rem;line-height:2.25rem}.c-card--major .c-card__title,.u-h2,.u-h3,h2{font-family:Harding,Palatino,serif;letter-spacing:-.0117156rem}.c-card--major .c-card__title,.u-h2,h2{-webkit-font-smoothing:antialiased;font-size:1.5rem;font-weight:700;line-height:1.6rem}.u-h3{font-size:1.25rem}.c-card__title,.c-reading-companion__figure-title,.u-h3,.u-h4,h4,h5,h6{-webkit-font-smoothing:antialiased;font-weight:700;line-height:1.4rem}.c-article-editorial-summary__container .c-article-editorial-summary__article-title,.c-card__title,h3{font-family:Harding,Palatino,serif;font-size:1.25rem}.c-article-editorial-summary__container .c-article-editorial-summary__article-title,h3{-webkit-font-smoothing:antialiased;font-weight:700;letter-spacing:-.0117156rem;line-height:1.4rem}.c-reading-companion__figure-title,.u-h4,h4{font-family:-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Oxygen-Sans,Ubuntu,Cantarell,Helvetica Neue,sans-serif;font-size:1.125rem;letter-spacing:-.0117156rem}button:focus{outline:3px solid #fece3e;will-change:transform}input+label{padding-left:.5em}nav ol,nav ul{list-style:none none}p:empty{display:none}.sans-serif{font-family:-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Oxygen-Sans,Ubuntu,Cantarell,Helvetica Neue,sans-serif}.article-page{background:#fff}.c-article-header{font-family:-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Oxygen-Sans,Ubuntu,Cantarell,Helvetica Neue,sans-serif;margin-bottom:40px}.c-article-identifiers{color:#6f6f6f;display:flex;flex-wrap:wrap;font-size:1rem;line-height:1.3;list-style:none;margin:0 0 8px;padding:0}.c-article-identifiers__item{border-right:1px solid #6f6f6f;list-style:none;margin-right:8px;padding-right:8px}.c-article-identifiers__item:last-child{border-right:0;margin-right:0;padding-right:0}.c-article-title{font-size:1.5rem;line-height:1.25;margin:0 0 16px}@media only screen and (min-width:768px){.c-article-title{font-size:1.875rem;line-height:1.2}}.c-article-author-list{display:inline;font-size:1rem;list-style:none;margin:0 8px 0 0;padding:0;width:100%}.c-article-author-list__item{display:inline;padding-right:0}.c-article-author-list svg{margin-left:4px}.c-article-author-list__show-more{display:none;margin-right:4px}.c-article-author-list__button,.js .c-article-author-list__item--hide,.js .c-article-author-list__show-more{display:none}.js .c-article-author-list--long .c-article-author-list__show-more,.js .c-article-author-list--long+.c-article-author-list__button{display:inline}@media only screen and (max-width:539px){.js .c-article-author-list__item--hide-small-screen{display:none}.js .c-article-author-list--short .c-article-author-list__show-more,.js .c-article-author-list--short+.c-article-author-list__button{display:inline}}#uptodate-client,.js .c-article-author-list--expanded .c-article-author-list__show-more{display:none!important}.js .c-article-author-list--expanded .c-article-author-list__item--hide-small-screen{display:inline!important}.c-article-author-list__button,.c-button-author-list{background:#ebf1f5;border:4px solid #ebf1f5;border-radius:20px;color:#666;font-size:.875rem;line-height:1.4;padding:2px 11px 2px 8px;text-decoration:none}.c-article-author-list__button svg,.c-button-author-list svg{margin:1px 4px 0 0}.c-article-author-list__button:hover,.c-button-author-list:hover{background:#069;border-color:transparent;color:#fff}.c-article-info-details{font-size:1rem;margin-bottom:8px;margin-top:16px}.c-article-info-details__cite-as{border-left:1px solid #6f6f6f;margin-left:8px;padding-left:8px}.c-article-metrics-bar{display:flex;flex-wrap:wrap;font-size:1rem;line-height:1.3}.c-article-metrics-bar__wrapper{margin:16px 0}.c-article-metrics-bar__item{align-items:baseline;border-right:1px solid #6f6f6f;margin-right:8px}.c-article-metrics-bar__item:last-child{border-right:0}.c-article-metrics-bar__count{font-weight:700;margin:0}.c-article-metrics-bar__label{color:#626262;font-style:normal;font-weight:400;margin:0 10px 0 5px}.c-article-metrics-bar__details{margin:0}.c-article-main-column{font-family:Harding,Palatino,serif;margin-right:8.6%;width:60.2%}@media only screen and (max-width:1023px){.c-article-main-column{margin-right:0;width:100%}}.c-article-extras{float:left;font-family:-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Oxygen-Sans,Ubuntu,Cantarell,Helvetica Neue,sans-serif;width:31.2%}@media only screen and (max-width:1023px){.c-article-extras{display:none}}.c-article-associated-content__container .c-article-associated-content__title,.c-article-section__title{border-bottom:2px solid #d5d5d5;font-size:1.25rem;margin:0;padding-bottom:8px}@media only screen and (min-width:768px){.c-article-associated-content__container .c-article-associated-content__title,.c-article-section__title{font-size:1.5rem;line-height:1.24}}.c-article-associated-content__container .c-article-associated-content__title{margin-bottom:8px}.c-article-body p{margin-bottom:24px;margin-top:0}.c-article-section{clear:both}.c-article-section__content{margin-bottom:40px;padding-top:8px}@media only screen and (max-width:1023px){.c-article-section__content{padding-left:0}}.c-article-authors-search{margin-bottom:24px;margin-top:0}.c-article-authors-search__item,.c-article-authors-search__title{font-family:-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Oxygen-Sans,Ubuntu,Cantarell,Helvetica Neue,sans-serif}.c-article-authors-search__title{color:#626262;font-size:1.05rem;font-weight:700;margin:0;padding:0}.c-article-authors-search__item{font-size:1rem}.c-article-authors-search__text{margin:0}.c-article-license__badge,c-card__section{margin-top:8px}.c-code-block{border:1px solid #eee;font-family:monospace;margin:0 0 24px;padding:20px}.c-code-block__heading{font-weight:400;margin-bottom:16px}.c-code-block__line{display:block;overflow-wrap:break-word;white-space:pre-wrap}.c-article-share-box__no-sharelink-info{font-size:.813rem;font-weight:700;margin-bottom:24px;padding-top:4px}.c-article-share-box__only-read-input{border:1px solid #d5d5d5;box-sizing:content-box;display:inline-block;font-size:.875rem;font-weight:700;height:24px;margin-bottom:8px;padding:8px 10px}.c-article-share-box__button--link-like{background-color:transparent;border:0;color:#069;cursor:pointer;font-size:.875rem;margin-bottom:8px;margin-left:10px}.c-article-editorial-summary__container{font-family:-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Oxygen-Sans,Ubuntu,Cantarell,Helvetica Neue,sans-serif;font-size:1rem}.c-article-editorial-summary__container .c-article-editorial-summary__content p:last-child{margin-bottom:0}.c-article-editorial-summary__container .c-article-editorial-summary__content--less{max-height:9.5rem;overflow:hidden}.c-article-editorial-summary__container .c-article-editorial-summary__button{background-color:#fff;border:0;color:#069;font-size:.875rem;margin-bottom:16px}.c-article-editorial-summary__container .c-article-editorial-summary__button.active,.c-article-editorial-summary__container .c-article-editorial-summary__button.hover,.c-article-editorial-summary__container .c-article-editorial-summary__button:active,.c-article-editorial-summary__container .c-article-editorial-summary__button:hover{text-decoration:underline;text-decoration-skip-ink:auto}.c-article-associated-content__container .c-article-associated-content__collection-label{font-size:.875rem;line-height:1.4}.c-article-associated-content__container .c-article-associated-content__collection-title{line-height:1.3}.c-context-bar{box-shadow:0 0 10px 0 rgba(51,51,51,.2);position:relative;width:100%}.c-context-bar__title{display:none}.c-reading-companion{clear:both;min-height:389px}.c-reading-companion__sticky{max-width:389px}.c-reading-companion__scroll-pane{margin:0;min-height:200px;overflow:hidden auto}.c-reading-companion__tabs{display:flex;flex-flow:row nowrap;font-size:1rem;list-style:none;margin:0 0 8px;padding:0}.c-reading-companion__tabs>li{flex-grow:1}.c-reading-companion__tab{background-color:#eee;border:1px solid #d5d5d5;border-image:initial;border-left-width:0;color:#069;font-size:1rem;padding:8px 8px 8px 15px;text-align:left;width:100%}.c-reading-companion__tabs li:first-child .c-reading-companion__tab{border-left-width:1px}.c-reading-companion__tab--active{background-color:#fff;border-bottom:1px solid #fff;color:#222;font-weight:700}.c-reading-companion__sections-list{list-style:none;padding:0}.c-reading-companion__figures-list,.c-reading-companion__references-list{list-style:none;min-height:389px;padding:0}.c-reading-companion__references-list--numeric{list-style:decimal inside}.c-reading-companion__sections-list{margin:0 0 8px;min-height:50px}.c-reading-companion__section-item{font-size:1rem;padding:0}.c-reading-companion__section-item a{display:block;line-height:1.5;overflow:hidden;padding:8px 0 8px 16px;text-overflow:ellipsis;white-space:nowrap}.c-reading-companion__figure-item{border-top:1px solid #d5d5d5;font-size:1rem;padding:16px 8px 16px 0}.c-reading-companion__figure-item:first-child{border-top:none;padding-top:8px}.c-reading-companion__reference-item{border-top:1px solid #d5d5d5;font-size:1rem;padding:8px 8px 8px 16px}.c-reading-companion__reference-item:first-child{border-top:none}.c-reading-companion__reference-item a{word-break:break-word}.c-reading-companion__reference-citation{display:inline}.c-reading-companion__reference-links{font-size:.813rem;font-weight:700;list-style:none;margin:8px 0 0;padding:0;text-align:right}.c-reading-companion__reference-links>a{display:inline-block;padding-left:8px}.c-reading-companion__reference-links>a:first-child{display:inline-block;padding-left:0}.c-reading-companion__figure-title{display:block;margin:0 0 8px}.c-reading-companion__figure-links{display:flex;justify-content:space-between;margin:8px 0 0}.c-reading-companion__figure-links>a{align-items:center;display:flex}.c-reading-companion__figure-full-link svg{height:.8em;margin-left:2px}.c-reading-companion__panel{border-top:none;display:none;margin-top:0;padding-top:0}.c-cod,.c-reading-companion__panel--active{display:block}.c-cod{font-size:1rem;width:100%}.c-cod__form{background:#ebf0f3}.c-cod__prompt{font-size:1.125rem;line-height:1.3;margin:0 0 24px}.c-cod__label{display:block;margin:0 0 4px}.c-cod__row{display:flex;margin:0 0 16px}.c-cod__row:last-child{margin:0}.c-cod__input{border:1px solid #d5d5d5;border-radius:2px;flex-basis:75%;flex-shrink:0;margin:0;padding:13px}.c-cod__input--submit{background-color:#069;border:1px solid #069;color:#fff;flex-shrink:1;margin-left:8px;transition:background-color .2s ease-out 0s,color .2s ease-out 0s}.c-cod__input--submit-single{flex-basis:100%;flex-shrink:0;margin:0}.c-cod__input--submit:focus,.c-cod__input--submit:hover{background-color:#fff;color:#069}.c-pdf-download__link .u-icon{padding-top:2px}.c-pdf-download{display:flex;margin-bottom:16px;max-height:48px}@media only screen and (min-width:540px){.c-pdf-download{max-height:none}}@media only screen and (min-width:1024px){.c-pdf-download{max-height:48px}}.c-pdf-download__link{display:flex;flex:1 1 0%}.c-pdf-download__link:hover{text-decoration:none}.c-pdf-download__text{padding-right:4px}@media only screen and (max-width:539px){.c-pdf-download__text{text-transform:capitalize}}@media only screen and (min-width:540px){.c-pdf-download__text{padding-right:8px}}.c-context-bar--sticky .c-pdf-download{display:block;margin-bottom:0;white-space:nowrap}@media only screen and (max-width:539px){.c-pdf-download .u-sticky-visually-hidden{clip:rect(0,0,0,0);border:0;height:1px;margin:-100%;overflow:hidden;padding:0;position:absolute!important;width:1px}}.c-pdf-container{display:flex;justify-content:flex-end}@media only screen and (max-width:539px){.c-pdf-container .c-pdf-download{display:flex;flex-basis:100%}}.c-pdf-container .c-pdf-download+.c-pdf-download{margin-left:16px}.c-article-extras .c-pdf-container .c-pdf-download{width:100%}.c-article-extras .c-pdf-container .c-pdf-download+.c-pdf-download{margin-left:0}@media only screen and (min-width:540px){.c-context-bar--sticky .c-pdf-download__link{align-items:center;flex:1 1 183px}}@media only screen and (max-width:320px){.c-context-bar--sticky .c-pdf-download__link{padding:16px}}.article-page--commercial .c-article-main-column .c-pdf-button__container .c-pdf-download{display:none}@media only screen and (max-width:1023px){.article-page--commercial .c-article-main-column .c-pdf-button__container .c-pdf-download{display:block}}.c-status-message--success{border-bottom:2px solid #00b8b0;justify-content:center;margin-bottom:16px;padding-bottom:8px}.c-recommendations-list__item .c-card{flex-basis:100%}.c-recommendations-list__item .c-card__image{align-items:baseline;flex:1 1 40%;margin:0 0 0 16px;max-width:150px}.c-recommendations-list__item .c-card__image img{border:1px solid #cedbe0;height:auto;min-height:0;position:static}@media only screen and (max-width:1023px){.c-recommendations-list__item .c-card__image{display:none}}.c-card__layout{display:flex;flex:1 1 auto;justify-content:space-between}.c-card__title-recommendation{-webkit-box-orient:vertical;-webkit-line-clamp:4;display:-webkit-box;font-size:1rem;font-weight:700;line-height:1.4;margin:0 0 8px;max-height:5.6em;overflow:hidden!important;text-overflow:ellipsis}.c-card__title-recommendation .c-card__link{color:inherit}.c-card__title-recommendation .c-card__link:hover{text-decoration:underline}.c-card__title-recommendation .MathJax_Display{display:inline!important}.c-card__link:not(.c-card__link--no-block-link):before{z-index:1}.c-article-metrics__heading a,.c-article-metrics__posts .c-card__title a,.c-article-recommendations-card__link{color:inherit}.c-recommendations-column-switch .c-meta{margin-top:auto}.c-article-recommendations-card__meta-type,.c-meta .c-meta__item:first-child{font-weight:700}.c-article-body .c-article-recommendations-card__authors{display:none;font-family:-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Oxygen-Sans,Ubuntu,Cantarell,Helvetica Neue,sans-serif;font-size:.875rem;line-height:1.5;margin:0 0 8px}@media only screen and (max-width:539px){.c-article-body .c-article-recommendations-card__authors{display:block;margin:0}}.c-article-metrics__posts .c-card__title{font-size:1.05rem}.c-article-metrics__posts .c-card__title+span{color:#6f6f6f;font-size:1rem}p{overflow-wrap:break-word;word-break:break-word}.c-ad{text-align:center}@media only screen and (min-width:320px){.c-ad{padding:8px}}.c-ad--728x90{background-color:#ccc;display:none}.c-ad--728x90 .c-ad__inner{min-height:calc(1.5em + 94px)}@media only screen and (min-width:768px){.js .c-ad--728x90{display:none}}.c-ad__label{color:#333;font-family:-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Oxygen-Sans,Ubuntu,Cantarell,Helvetica Neue,sans-serif;font-size:.875rem;font-weight:400;line-height:1.5;margin-bottom:4px}.c-author-list{color:#6f6f6f;font-family:inherit;font-size:1rem;line-height:inherit;list-style:none;margin:0;padding:0}.c-author-list>li,.c-breadcrumbs>li,.c-footer__links>li,.js .c-author-list,.u-list-comma-separated>li,.u-list-inline>li{display:inline}.c-author-list>li:not(:first-child):not(:last-child):before{content:", "}.c-author-list>li:not(:only-child):last-child:before{content:" & "}.c-author-list--compact{font-size:.875rem;line-height:1.4}.c-author-list--truncated>li:not(:only-child):last-child:before{content:" ... "}.js .c-author-list__hide{display:none;visibility:hidden}.js .c-author-list__hide:first-child+*{margin-block-start:0}.c-meta{color:inherit;font-family:-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Oxygen-Sans,Ubuntu,Cantarell,Helvetica Neue,sans-serif;font-size:.875rem;line-height:1.4;list-style:none;margin:0;padding:0}.c-meta--large{font-size:1rem}.c-meta--large .c-meta__item{margin-bottom:8px}.c-meta__item{display:inline-block;margin-bottom:4px}.c-meta__item:not(:last-child){border-right:1px solid #d5d5d5;margin-right:4px;padding-right:4px}@media only screen and (max-width:539px){.c-meta__item--block-sm-max{display:block}.c-meta__item--block-sm-max:not(:last-child){border-right:none;margin-right:0;padding-right:0}}@media only screen and (min-width:1024px){.c-meta__item--block-at-lg{display:block}.c-meta__item--block-at-lg:not(:last-child){border-right:none;margin-right:0;padding-right:0}}.c-meta__type{font-weight:700;text-transform:none}.c-skip-link{background:#069;bottom:auto;color:#fff;font-family:-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Oxygen-Sans,Ubuntu,Cantarell,Helvetica Neue,sans-serif;font-size:.875rem;padding:8px;position:absolute;text-align:center;transform:translateY(-100%);z-index:9999}@media (prefers-reduced-motion:reduce){.c-skip-link{transition:top .3s ease-in-out 0s}}@media print{.c-skip-link{display:none}}.c-skip-link:link{color:#fff}.c-status-message{align-items:center;box-sizing:border-box;display:flex;font-family:-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Oxygen-Sans,Ubuntu,Cantarell,Helvetica Neue,sans-serif;font-size:1rem;position:relative;width:100%}.c-card__summary>p:last-child,.c-status-message :last-child{margin-bottom:0}.c-status-message--boxed{background-color:#fff;border:1px solid #eee;border-radius:2px;line-height:1.4;padding:16px}.c-status-message__heading{font-family:-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Oxygen-Sans,Ubuntu,Cantarell,Helvetica Neue,sans-serif;font-size:1rem;font-weight:700}.c-status-message__icon{fill:currentcolor;display:inline-block;flex:0 0 auto;height:1.5em;margin-right:8px;transform:translate(0);vertical-align:text-top;width:1.5em}.c-status-message__icon--top{align-self:flex-start}.c-status-message--info .c-status-message__icon{color:#003f8d}.c-status-message--boxed.c-status-message--info{border-bottom:4px solid #003f8d}.c-status-message--error .c-status-message__icon{color:#c40606}.c-status-message--boxed.c-status-message--error{border-bottom:4px solid #c40606}.c-status-message--success .c-status-message__icon{color:#00b8b0}.c-status-message--boxed.c-status-message--success{border-bottom:4px solid #00b8b0}.c-status-message--warning .c-status-message__icon{color:#edbc53}.c-status-message--boxed.c-status-message--warning{border-bottom:4px solid #edbc53}.c-breadcrumbs{color:#000;font-family:-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Oxygen-Sans,Ubuntu,Cantarell,Helvetica Neue,sans-serif;font-size:1rem;list-style:none;margin:0;padding:0}.c-breadcrumbs__link{color:#666}svg.c-breadcrumbs__chevron{fill:#888;height:10px;margin:4px 4px 0;width:10px}@media only screen and (max-width:539px){.c-breadcrumbs .c-breadcrumbs__item{display:none}.c-breadcrumbs .c-breadcrumbs__item:last-child,.c-breadcrumbs .c-breadcrumbs__item:nth-last-child(2){display:inline}}.c-card{background-color:transparent;border:0;box-shadow:none;display:flex;flex-direction:column;font-size:14px;min-width:0;overflow:hidden;padding:0;position:relative}.c-card--no-shape{background:0 0;border:0;box-shadow:none}.c-card__image{display:flex;justify-content:center;overflow:hidden;padding-bottom:56.25%;position:relative}@supports (aspect-ratio:1/1){.c-card__image{padding-bottom:0}}.c-card__image img{left:0;min-height:100%;min-width:100%;position:absolute}@supports ((-o-object-fit:cover) or (object-fit:cover)){.c-card__image img{height:100%;object-fit:cover;width:100%}}.c-card__body{flex:1 1 auto;padding:16px}.c-card--no-shape .c-card__body{padding:0}.c-card--no-shape .c-card__body:not(:first-child){padding-top:16px}.c-card__title{letter-spacing:-.01875rem;margin-bottom:8px;margin-top:0}[lang=de] .c-card__title{hyphens:auto}.c-card__summary{line-height:1.4}.c-card__summary>p{margin-bottom:5px}.c-card__summary a{text-decoration:underline}.c-card__link:not(.c-card__link--no-block-link):before{bottom:0;content:"";left:0;position:absolute;right:0;top:0}.c-card--flush .c-card__body{padding:0}.c-card--major{font-size:1rem}.c-card--dark{background-color:#29303c;border-width:0;color:#e3e4e5}.c-card--dark .c-card__title{color:#fff}.c-card--dark .c-card__link,.c-card--dark .c-card__summary a{color:inherit}.c-header{background-color:#fff;border-bottom:5px solid #000;font-size:1rem;line-height:1.4;margin-bottom:16px}.c-header__row{padding:0;position:relative}.c-header__row:not(:last-child){border-bottom:1px solid #eee}.c-header__split{align-items:center;display:flex;justify-content:space-between}.c-header__logo-container{flex:1 1 0px;line-height:0;margin:8px 24px 8px 0}.c-header__logo{transform:translateZ(0)}.c-header__logo img{max-height:32px}.c-header__container{margin:0 auto;max-width:1280px}.c-header__menu{align-items:center;display:flex;flex:0 1 auto;flex-wrap:wrap;font-weight:700;gap:8px 8px;line-height:1.4;list-style:none;margin:0 -8px;padding:0}@media print{.c-header__menu{display:none}}@media only screen and (max-width:1023px){.c-header__menu--hide-lg-max{display:none;visibility:hidden}}.c-header__menu--global{font-weight:400;justify-content:flex-end}.c-header__menu--global svg{display:none;visibility:hidden}.c-header__menu--global svg:first-child+*{margin-block-start:0}@media only screen and (min-width:540px){.c-header__menu--global svg{display:block;visibility:visible}}.c-header__menu--journal{font-size:.875rem;margin:8px 0 8px -8px}@media only screen and (min-width:540px){.c-header__menu--journal{flex-wrap:nowrap;font-size:1rem}}.c-header__item{padding-bottom:0;padding-top:0;position:static}.c-header__item--pipe{border-left:2px solid #eee;padding-left:8px}.c-header__item--padding{padding-bottom:8px;padding-top:8px}@media only screen and (min-width:540px){.c-header__item--dropdown-menu{position:relative}}@media only screen and (min-width:1024px){.c-header__item--hide-lg{display:none;visibility:hidden}}@media only screen and (max-width:767px){.c-header__item--hide-md-max{display:none;visibility:hidden}.c-header__item--hide-md-max:first-child+*{margin-block-start:0}}.c-header__link{align-items:center;color:inherit;display:inline-flex;gap:4px 4px;padding:8px;white-space:nowrap}.c-header__link svg{transition-duration:.2s}.c-header__show-text{display:none;visibility:hidden}.has-tethered .c-header__heading--js-hide:first-child+*{margin-block-start:0}@media only screen and (min-width:540px){.c-header__show-text{display:inline;visibility:visible}}.c-header__dropdown{background-color:#000;border-bottom:1px solid #2f2f2f;color:#eee;font-size:.875rem;line-height:1.2;padding:16px 0}@media print{.c-header__dropdown{display:none}}.c-header__heading{display:inline-block;font-family:-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Oxygen-Sans,Ubuntu,Cantarell,Helvetica Neue,sans-serif;font-size:1.25rem;font-weight:400;line-height:1.4;margin-bottom:8px}.c-header__heading--keyline{border-top:1px solid;border-color:#2f2f2f;margin-top:16px;padding-top:16px;width:100%}.c-header__list{display:flex;flex-wrap:wrap;gap:0 16px;list-style:none;margin:0 -8px}.c-header__flush{margin:0 -8px}.c-header__visually-hidden{clip:rect(0,0,0,0);border:0;height:1px;margin:-100%;overflow:hidden;padding:0;position:absolute!important;width:1px}.c-header__search-form{margin-bottom:8px}.c-header__search-layout{display:flex;flex-wrap:wrap;gap:16px 16px}.c-header__search-layout>:first-child{flex:999 1 auto}.c-header__search-layout>*{flex:1 1 auto}.c-header__search-layout--max-width{max-width:720px}.c-header__search-button{align-items:center;background-color:transparent;background-image:none;border:1px solid #fff;border-radius:2px;color:#fff;cursor:pointer;display:flex;font-family:sans-serif;font-size:1rem;justify-content:center;line-height:1.15;margin:0;padding:8px 16px;position:relative;text-decoration:none;transition:all .25s ease 0s,color .25s ease 0s,border-color .25s ease 0s;width:100%}.u-button svg,.u-button--primary svg{fill:currentcolor}.c-header__input,.c-header__select{border:1px solid;border-radius:3px;box-sizing:border-box;font-size:1rem;padding:8px 16px;width:100%}.c-header__select{-webkit-appearance:none;background-image:url("data:image/svg+xml,%3Csvg height='16' viewBox='0 0 16 16' width='16' xmlns='http://www.w3.org/2000/svg'%3E%3Cpath d='m5.58578644 3-3.29289322-3.29289322c-.39052429-.39052429-.39052429-1.02368927 0-1.41421356s1.02368927-.39052429 1.41421356 0l4 4c.39052429.39052429.39052429 1.02368927 0 1.41421356l-4 4c-.39052429.39052429-1.02368927.39052429-1.41421356 0s-.39052429-1.02368927 0-1.41421356z' fill='%23333' fill-rule='evenodd' transform='matrix(0 1 -1 0 11 3)'/%3E%3C/svg%3E");background-position:right .7em top 50%;background-repeat:no-repeat;background-size:1em;box-shadow:0 1px 0 1px rgba(0,0,0,.04);display:block;margin:0;max-width:100%;min-width:150px}@media only screen and (min-width:540px){.c-header__menu--journal .c-header__item--dropdown-menu:last-child .c-header__dropdown.has-tethered{left:auto;right:0}}@media only screen and (min-width:768px){.c-header__menu--journal .c-header__item--dropdown-menu:last-child .c-header__dropdown.has-tethered{left:0;right:auto}}.c-header__dropdown.has-tethered{border-bottom:0;border-radius:0 0 2px 2px;left:0;position:absolute;top:100%;transform:translateY(5px);width:100%;z-index:1}@media only screen and (min-width:540px){.c-header__dropdown.has-tethered{transform:translateY(8px);width:auto}}@media only screen and (min-width:768px){.c-header__dropdown.has-tethered{min-width:225px}}.c-header__dropdown--full-width.has-tethered{padding:32px 0 24px;transform:none;width:100%}.has-tethered .c-header__heading--js-hide{display:none;visibility:hidden}.has-tethered .c-header__list--js-stack{flex-direction:column}.has-tethered .c-header__item--keyline,.has-tethered .c-header__list~.c-header__list .c-header__item:first-child{border-top:1px solid #d5d5d5;margin-top:8px;padding-top:8px}.c-header__item--snid-account-widget{display:flex}.c-header__container{padding:0 4px}.c-header__list{padding:0 12px}.c-header__menu .c-header__link{font-size:14px}.c-header__item--snid-account-widget .c-header__link{padding:8px}.c-header__menu--journal{margin-left:0}@media only screen and (min-width:540px){.c-header__container{padding:0 16px}.c-header__menu--journal{margin-left:-8px}.c-header__menu .c-header__link{font-size:16px}.c-header__link--search{gap:13px 13px}}.u-button{align-items:center;background-color:transparent;background-image:none;border:1px solid #069;border-radius:2px;color:#069;cursor:pointer;display:inline-flex;font-family:sans-serif;font-size:1rem;justify-content:center;line-height:1.3;margin:0;padding:8px;position:relative;text-decoration:none;transition:all .25s ease 0s,color .25s ease 0s,border-color .25s ease 0s;width:auto}.u-button--primary{background-color:#069;background-image:none;border:1px solid #069;color:#fff}.u-button--full-width{display:flex;width:100%}.u-display-none{display:none}.js .u-js-hide,.u-hide{display:none;visibility:hidden}.u-hide:first-child+*{margin-block-start:0}.u-visually-hidden{clip:rect(0,0,0,0);border:0;height:1px;margin:-100%;overflow:hidden;padding:0;position:absolute!important;width:1px}@media print{.u-hide-print{display:none}}@media only screen and (min-width:1024px){.u-hide-at-lg{display:none;visibility:hidden}.u-hide-at-lg:first-child+*{margin-block-start:0}}.u-clearfix:after,.u-clearfix:before{content:"";display:table}.u-clearfix:after{clear:both}.u-color-open-access{color:#b74616}.u-float-left{float:left}.u-icon{fill:currentcolor;display:inline-block;height:1em;transform:translate(0);vertical-align:text-top;width:1em}.u-full-height{height:100%}.u-list-reset{list-style:none;margin:0;padding:0}.u-sans-serif{font-family:-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Oxygen-Sans,Ubuntu,Cantarell,Helvetica Neue,sans-serif}.u-container{margin:0 auto;max-width:1280px;padding:0 16px}.u-justify-content-space-between{justify-content:space-between}.u-mt-32{margin-top:32px}.u-mb-8{margin-bottom:8px}.u-mb-16{margin-bottom:16px}.u-mb-24{margin-bottom:24px}.u-mb-32{margin-bottom:32px}.c-nature-box svg+.c-article__button-text,.u-ml-8{margin-left:8px}.u-pa-16{padding:16px}html *,html :after,html :before{box-sizing:inherit}.c-article-section__title,.c-article-title{font-weight:700}.c-card__title{line-height:1.4em}.c-article__button{background-color:#069;border:1px solid #069;border-radius:2px;color:#fff;display:flex;font-family:-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Oxygen-Sans,Ubuntu,Cantarell,Helvetica Neue,sans-serif;font-size:.875rem;line-height:1.4;margin-bottom:16px;padding:13px;transition:background-color .2s ease-out 0s,color .2s ease-out 0s}.c-article__button,.c-article__button:hover{text-decoration:none}.c-article__button--inverted,.c-article__button:hover{background-color:#fff;color:#069}.c-article__button--inverted:hover{background-color:#069;color:#fff}.c-header__link{text-decoration:inherit}.grade-c-hide{display:block}.u-lazy-ad-wrapper{background-color:#ccc;display:none;min-height:137px}@media only screen and (min-width:768px){.u-lazy-ad-wrapper{display:block}}.c-nature-box{background-color:#fff;border:1px solid #d5d5d5;border-radius:2px;box-shadow:0 0 5px 0 rgba(51,51,51,.1);line-height:1.3;margin-bottom:24px;padding:16px 16px 3px}.c-nature-box__text{font-size:1rem;margin-bottom:16px}.c-nature-box .c-pdf-download{margin-bottom:16px!important}.c-nature-box--version{background-color:#eee}.c-nature-box__wrapper{transform:translateZ(0)}.c-nature-box__wrapper--placeholder{min-height:165px}.c-pdf-download__link{padding:13px 24px} } </style> <link data-test="critical-css-handler" data-inline-css-source="critical-css" rel="stylesheet" href="/static/css/enhanced-article-nature-branded-68c4876c28.css" media="print" onload="this.media='only print, only all and (prefers-color-scheme: no-preference), only all and (prefers-color-scheme: light), only all and (prefers-color-scheme: dark)';this.onload=null"> <noscript> <link rel="stylesheet" type="text/css" href="/static/css/enhanced-article-nature-branded-68c4876c28.css" media="only print, only all and (prefers-color-scheme: no-preference), only all and (prefers-color-scheme: light), only all and (prefers-color-scheme: dark)"> </noscript> <link rel="stylesheet" type="text/css" href="/static/css/article-print-122346e276.css" media="print"> <link rel="apple-touch-icon" sizes="180x180" href=/static/images/favicons/nature/apple-touch-icon-f39cb19454.png> <link rel="icon" type="image/png" sizes="48x48" href=/static/images/favicons/nature/favicon-48x48-b52890008c.png> <link rel="icon" type="image/png" sizes="32x32" href=/static/images/favicons/nature/favicon-32x32-3fe59ece92.png> <link rel="icon" type="image/png" sizes="16x16" href=/static/images/favicons/nature/favicon-16x16-951651ab72.png> <link rel="manifest" href=/static/manifest.json crossorigin="use-credentials"> <link rel="mask-icon" href=/static/images/favicons/nature/safari-pinned-tab-69bff48fe6.svg color="#000000"> <link rel="shortcut icon" href=/static/images/favicons/nature/favicon.ico> <meta name="msapplication-TileColor" content="#000000"> <meta name="msapplication-config" content=/static/browserconfig.xml> <meta name="theme-color" content="#000000"> <meta name="application-name" content="Nature"> <script> (function () { if ( typeof window.CustomEvent === "function" ) return false; function CustomEvent ( event, params ) { params = params || { bubbles: false, cancelable: false, detail: null }; var evt = document.createEvent( 'CustomEvent' ); evt.initCustomEvent( event, params.bubbles, params.cancelable, params.detail ); return evt; } CustomEvent.prototype = window.Event.prototype; window.CustomEvent = CustomEvent; })(); </script>  <script data-test="gtm-head"> window.initGTM = function() { if (window.config.mustardcut) { (function (w, d, s, l, i) { w[l] = w[l] || []; w[l].push({'gtm.start': new Date().getTime(), event: 'gtm.js'}); var f = d.getElementsByTagName(s)[0], j = d.createElement(s), dl = l != 'dataLayer' ? '&l=' + l : ''; j.async = true; j.src = 'https://www.googletagmanager.com/gtm.js?id=' + i + dl; f.parentNode.insertBefore(j, f); })(window, document, 'script', 'dataLayer', 'GTM-MRVXSHQ'); } } </script>  <script> (function(w,d,t) { function cc() { var h = w.location.hostname; if (h.indexOf('preview-www.nature.com') > -1) return; var e = d.createElement(t), s = d.getElementsByTagName(t)[0]; if (h.indexOf('nature.com') > -1) { if (h.indexOf('test-www.nature.com') > -1) { e.src = 'https://cmp.nature.com/production_live/en/consent-bundle-8-68.js'; e.setAttribute('onload', "initGTM(window,document,'script','dataLayer','GTM-MRVXSHQ')"); } else { e.src = 'https://cmp.nature.com/production_live/en/consent-bundle-8-68.js'; e.setAttribute('onload', "initGTM(window,document,'script','dataLayer','GTM-MRVXSHQ')"); } } else { e.src = '/static/js/cookie-consent-es5-bundle-cb57c2c98a.js'; e.setAttribute('data-consent', h); } s.insertAdjacentElement('afterend', e); } cc(); })(window,document,'script'); </script> <script id="js-position0"> (function(w, d) { w.idpVerifyPrefix = 'https://verify.nature.com'; w.ra21Host = 'https://wayf.springernature.com'; var moduleSupport = (function() { return 'noModule' in d.createElement('script'); })(); if (w.config.mustardcut === true) { w.loader = { index: 0, registered: [], scripts: [ {src: '/static/js/global-article-es6-bundle-c8a573ca90.js', test: 'global-article-js', module: true}, {src: '/static/js/global-article-es5-bundle-d17603b9e9.js', test: 'global-article-js', nomodule: true}, {src: '/static/js/shared-es6-bundle-606cb67187.js', test: 'shared-js', module: true}, {src: '/static/js/shared-es5-bundle-e919764a53.js', test: 'shared-js', nomodule: true}, {src: '/static/js/header-150-es6-bundle-5bb959eaa1.js', test: 'header-150-js', module: true}, {src: '/static/js/header-150-es5-bundle-994fde5b1d.js', test: 'header-150-js', nomodule: true} ].filter(function (s) { if (s.src === null) return false; if (moduleSupport && s.nomodule) return false; return !(!moduleSupport && s.module); }), register: function (value) { this.registered.push(value); }, ready: function () { if (this.registered.length === this.scripts.length) { this.registered.forEach(function (fn) { if (typeof fn === 'function') { setTimeout(fn, 0); } }); this.ready = function () {}; } }, insert: function (s) { var t = d.getElementById('js-position' + this.index); if (t && t.insertAdjacentElement) { t.insertAdjacentElement('afterend', s); } else { d.head.appendChild(s); } ++this.index; }, createScript: function (script, beforeLoad) { var s = d.createElement('script'); s.id = 'js-position' + (this.index + 1); s.setAttribute('data-test', script.test); if (beforeLoad) { s.defer = 'defer'; s.onload = function () { if (script.noinit) { loader.register(true); } if (d.readyState === 'interactive' || d.readyState === 'complete') { loader.ready(); } }; } else { s.async = 'async'; } s.src = script.src; return s; }, init: function () { this.scripts.forEach(function (s) { loader.insert(loader.createScript(s, true)); }); d.addEventListener('DOMContentLoaded', function () { loader.ready(); var conditionalScripts; conditionalScripts = [ {match: 'div[data-pan-container]', src: '/static/js/pan-zoom-es6-bundle-464a2af269.js', test: 'pan-zoom-js', module: true }, {match: 'div[data-pan-container]', src: '/static/js/pan-zoom-es5-bundle-98fb9b653b.js', test: 'pan-zoom-js', nomodule: true }, {match: 'math,span.mathjax-tex', src: '/static/js/math-es6-bundle-23597ae350.js', test: 'math-js', module: true}, {match: 'math,span.mathjax-tex', src: '/static/js/math-es5-bundle-6532c6f78b.js', test: 'math-js', nomodule: true} ]; if (conditionalScripts) { conditionalScripts.filter(function (script) { return !!document.querySelector(script.match) && !((moduleSupport && script.nomodule) || (!moduleSupport && script.module)); }).forEach(function (script) { loader.insert(loader.createScript(script)); }); } }, false); } }; loader.init(); } })(window, document); </script> <meta name="robots" content="noarchive"> <meta name="access" content="Yes"> <link rel="search" href="https://www.nature.com/search"> <link rel="search" href="https://www.nature.com/opensearch/opensearch.xml" type="application/opensearchdescription+xml" title="nature.com"> <link rel="search" href="https://www.nature.com/opensearch/request" type="application/sru+xml" title="nature.com"> <script type="application/ld+json">{"mainEntity":{"headline":"Addendum: A graph placement methodology for fast chip design","description":"","datePublished":"2024-09-26T00:00:00Z","dateModified":"2024-09-26T00:00:00Z","pageStart":"E10","pageEnd":"E11","sameAs":"https://doi.org/10.1038/s41586-024-08032-5","keywords":["Computational science","Electrical and electronic engineering","Science","Humanities and Social Sciences","multidisciplinary"],"image":[],"isPartOf":{"name":"Nature","issn":["1476-4687","0028-0836"],"volumeNumber":"634","@type":["Periodical","PublicationVolume"]},"publisher":{"name":"Nature Publishing Group UK","logo":{"url":"https://www.springernature.com/app-sn/public/images/logo-springernature.png","@type":"ImageObject"},"@type":"Organization"},"author":[{"name":"Anna Goldie","url":"http://orcid.org/0000-0002-4887-6293","affiliation":[{"name":"Google Research, Brain Team, Google","address":{"name":"Google Research, Brain Team, Google, Mountain View, USA","@type":"PostalAddress"},"@type":"Organization"},{"name":"Stanford University","address":{"name":"Computer Science Department, Stanford University, Stanford, USA","@type":"PostalAddress"},"@type":"Organization"}],"email":"agoldie@google.com","@type":"Person"},{"name":"Azalia Mirhoseini","url":"http://orcid.org/0000-0002-2440-0944","affiliation":[{"name":"Google Research, Brain Team, Google","address":{"name":"Google Research, Brain Team, Google, Mountain View, USA","@type":"PostalAddress"},"@type":"Organization"},{"name":"Stanford University","address":{"name":"Computer Science Department, Stanford University, Stanford, USA","@type":"PostalAddress"},"@type":"Organization"}],"email":"azalia@google.com","@type":"Person"},{"name":"Mustafa Yazgan","affiliation":[{"name":"Google Chip Implementation and Infrastructure (CI2) Team, Google","address":{"name":"Google Chip Implementation and Infrastructure (CI2) Team, Google, Sunnyvale, USA","@type":"PostalAddress"},"@type":"Organization"}],"@type":"Person"},{"name":"Joe Wenjie Jiang","affiliation":[{"name":"Google Research, Brain Team, Google","address":{"name":"Google Research, Brain Team, Google, Mountain View, USA","@type":"PostalAddress"},"@type":"Organization"}],"@type":"Person"},{"name":"Ebrahim Songhori","affiliation":[{"name":"Google Research, Brain Team, Google","address":{"name":"Google Research, Brain Team, Google, Mountain View, USA","@type":"PostalAddress"},"@type":"Organization"}],"@type":"Person"},{"name":"Shen Wang","affiliation":[{"name":"Google Research, Brain Team, Google","address":{"name":"Google Research, Brain Team, Google, Mountain View, USA","@type":"PostalAddress"},"@type":"Organization"}],"@type":"Person"},{"name":"Young-Joon Lee","affiliation":[{"name":"Google Chip Implementation and Infrastructure (CI2) Team, Google","address":{"name":"Google Chip Implementation and Infrastructure (CI2) Team, Google, Sunnyvale, USA","@type":"PostalAddress"},"@type":"Organization"}],"@type":"Person"},{"name":"Eric Johnson","affiliation":[{"name":"Google Research, Brain Team, Google","address":{"name":"Google Research, Brain Team, Google, Mountain View, USA","@type":"PostalAddress"},"@type":"Organization"}],"@type":"Person"},{"name":"Omkar Pathak","affiliation":[{"name":"Google Chip Implementation and Infrastructure (CI2) Team, Google","address":{"name":"Google Chip Implementation and Infrastructure (CI2) Team, Google, Sunnyvale, USA","@type":"PostalAddress"},"@type":"Organization"}],"@type":"Person"},{"name":"Azade Nova","affiliation":[{"name":"Google Research, Brain Team, Google","address":{"name":"Google Research, Brain Team, Google, Mountain View, USA","@type":"PostalAddress"},"@type":"Organization"}],"@type":"Person"},{"name":"Jiwoo Pak","affiliation":[{"name":"Google Chip Implementation and Infrastructure (CI2) Team, Google","address":{"name":"Google Chip Implementation and Infrastructure (CI2) Team, Google, Sunnyvale, USA","@type":"PostalAddress"},"@type":"Organization"}],"@type":"Person"},{"name":"Andy Tong","affiliation":[{"name":"Google Chip Implementation and Infrastructure (CI2) Team, Google","address":{"name":"Google Chip Implementation and Infrastructure (CI2) Team, Google, Sunnyvale, USA","@type":"PostalAddress"},"@type":"Organization"}],"@type":"Person"},{"name":"Kavya Srinivasa","affiliation":[{"name":"Google Chip Implementation and Infrastructure (CI2) Team, Google","address":{"name":"Google Chip Implementation and Infrastructure (CI2) Team, Google, Sunnyvale, USA","@type":"PostalAddress"},"@type":"Organization"}],"@type":"Person"},{"name":"William Hang","affiliation":[{"name":"Stanford University","address":{"name":"Computer Science Department, Stanford University, Stanford, USA","@type":"PostalAddress"},"@type":"Organization"}],"@type":"Person"},{"name":"Emre Tuncer","affiliation":[{"name":"Google Chip Implementation and Infrastructure (CI2) Team, Google","address":{"name":"Google Chip Implementation and Infrastructure (CI2) Team, Google, Sunnyvale, USA","@type":"PostalAddress"},"@type":"Organization"}],"@type":"Person"},{"name":"Quoc V. Le","affiliation":[{"name":"Google Research, Brain Team, Google","address":{"name":"Google Research, Brain Team, Google, Mountain View, USA","@type":"PostalAddress"},"@type":"Organization"}],"@type":"Person"},{"name":"James Laudon","url":"http://orcid.org/0000-0003-1061-1780","affiliation":[{"name":"Google Research, Brain Team, Google","address":{"name":"Google Research, Brain Team, Google, Mountain View, USA","@type":"PostalAddress"},"@type":"Organization"}],"@type":"Person"},{"name":"Richard Ho","affiliation":[{"name":"Google Chip Implementation and Infrastructure (CI2) Team, Google","address":{"name":"Google Chip Implementation and Infrastructure (CI2) Team, Google, Sunnyvale, USA","@type":"PostalAddress"},"@type":"Organization"}],"@type":"Person"},{"name":"Roger Carpenter","affiliation":[{"name":"Google Chip Implementation and Infrastructure (CI2) Team, Google","address":{"name":"Google Chip Implementation and Infrastructure (CI2) Team, Google, Sunnyvale, USA","@type":"PostalAddress"},"@type":"Organization"}],"@type":"Person"},{"name":"Jeff Dean","affiliation":[{"name":"Google Research, Brain Team, Google","address":{"name":"Google Research, Brain Team, Google, Mountain View, USA","@type":"PostalAddress"},"@type":"Organization"}],"@type":"Person"}],"isAccessibleForFree":false,"hasPart":{"isAccessibleForFree":false,"cssSelector":".main-content","@type":"WebPageElement"},"@type":"ScholarlyArticle"},"@context":"https://schema.org","@type":"WebPage"}</script> <link rel="canonical" href="https://www.nature.com/articles/s41586-024-08032-5"> <meta name="journal_id" content="41586"/> <meta name="dc.title" content="Addendum: A graph placement methodology for fast chip design"/> <meta name="dc.source" content="Nature 2024 634:8034"/> <meta name="dc.format" content="text/html"/> <meta name="dc.publisher" content="Nature Publishing Group"/> <meta name="dc.date" content="2024-09-26"/> <meta name="dc.type" content="BriefCommunication"/> <meta name="dc.language" content="En"/> <meta name="dc.copyright" content="2024 The Author(s), under exclusive licence to Springer Nature Limited"/> <meta name="dc.rights" content="2024 The Author(s), under exclusive licence to Springer Nature Limited"/> <meta name="dc.rightsAgent" content="journalpermissions@springernature.com"/> <meta name="dc.description" content=""/> <meta name="prism.issn" content="1476-4687"/> <meta name="prism.publicationName" content="Nature"/> <meta name="prism.publicationDate" content="2024-09-26"/> <meta name="prism.volume" content="634"/> <meta name="prism.number" content="8034"/> <meta name="prism.section" content="BriefCommunication"/> <meta name="prism.startingPage" content="E10"/> <meta name="prism.endingPage" content="E11"/> <meta name="prism.copyright" content="2024 The Author(s), under exclusive licence to Springer Nature Limited"/> <meta name="prism.rightsAgent" content="journalpermissions@springernature.com"/> <meta name="prism.url" content="https://www.nature.com/articles/s41586-024-08032-5"/> <meta name="prism.doi" content="doi:10.1038/s41586-024-08032-5"/> <meta name="citation_pdf_url" content="https://www.nature.com/articles/s41586-024-08032-5.pdf"/> <meta name="citation_fulltext_html_url" content="https://www.nature.com/articles/s41586-024-08032-5"/> <meta name="citation_journal_title" content="Nature"/> <meta name="citation_journal_abbrev" content="Nature"/> <meta name="citation_publisher" content="Nature Publishing Group"/> <meta name="citation_issn" content="1476-4687"/> <meta name="citation_title" content="Addendum: A graph placement methodology for fast chip design"/> <meta name="citation_volume" content="634"/> <meta name="citation_issue" content="8034"/> <meta name="citation_publication_date" content="2024/10"/> <meta name="citation_online_date" content="2024/09/26"/> <meta name="citation_firstpage" content="E10"/> <meta name="citation_lastpage" content="E11"/> <meta name="citation_article_type" content="Addendum"/> <meta name="citation_language" content="en"/> <meta name="dc.identifier" content="doi:10.1038/s41586-024-08032-5"/> <meta name="DOI" content="10.1038/s41586-024-08032-5"/> <meta name="size" content="45094"/> <meta name="citation_doi" content="10.1038/s41586-024-08032-5"/> <meta name="citation_springer_api_url" content="http://api.springer.com/xmldata/jats?q=doi:10.1038/s41586-024-08032-5&api_key="/> <meta name="description" content=""/> <meta name="dc.creator" content="Goldie, Anna"/> <meta name="dc.creator" content="Mirhoseini, Azalia"/> <meta name="dc.creator" content="Yazgan, Mustafa"/> <meta name="dc.creator" content="Jiang, Joe Wenjie"/> <meta name="dc.creator" content="Songhori, Ebrahim"/> <meta name="dc.creator" content="Wang, Shen"/> <meta name="dc.creator" content="Lee, Young-Joon"/> <meta name="dc.creator" content="Johnson, Eric"/> <meta name="dc.creator" content="Pathak, Omkar"/> <meta name="dc.creator" content="Nova, Azade"/> <meta name="dc.creator" content="Pak, Jiwoo"/> <meta name="dc.creator" content="Tong, Andy"/> <meta name="dc.creator" content="Srinivasa, Kavya"/> <meta name="dc.creator" content="Hang, William"/> <meta name="dc.creator" content="Tuncer, Emre"/> <meta name="dc.creator" content="Le, Quoc V."/> <meta name="dc.creator" content="Laudon, James"/> <meta name="dc.creator" content="Ho, Richard"/> <meta name="dc.creator" content="Carpenter, Roger"/> <meta name="dc.creator" content="Dean, Jeff"/> <meta name="dc.subject" content="Computational science"/> <meta name="dc.subject" content="Electrical and electronic engineering"/> <meta name="citation_reference" content="Mirhoseini, A. & Goldie, A. et al. Chip placement with deep reinforcement learning. Preprint at https://doi.org/10.48550/arXiv.2004.10746 (2020)."/> <meta name="citation_reference" content="Lu, Y. C. et al. RL-CCD: concurrent clock and data optimization using attention-based self-supervised reinforcement learning. In Proc. 60th ACM/IEEE Design Automation Conference 1–6 (IEEE, 2023)."/> <meta name="citation_reference" content="Lai, Y. et al. Chipformer: transferable chip placement via offline decision transformer. In Proc. 40th International Conference on Machine Learning 18319–18345 (JMLR.org, 2023)."/> <meta name="citation_reference" content="Shi, Y., Xue, K., Song, L. & Qian, C. Macro placement by wire-mask-guided black-box optimization. In Proc. 37th International Conference on Neural Information Processing Systems 6825–6843 (Curran Associates, 2024)."/> <meta name="citation_reference" content="Lai, Y., Yao, M. & Ping, L. Maskplace: fast chip placement via reinforced visual representation learning. In Proc. 36th International Conference on Neural Information Processing Systems 24019–24030 (Curran Associates, 2024)."/> <meta name="citation_reference" content="Cheng, R. & Yan, J. On joint learning for solving placement and routing in chip design. In Proc. 35th International Conference on Neural Information Processing Systems 16508–16519 (Curran Associates, 2024)."/> <meta name="citation_reference" content="Chang, F.-C. et al. Flexible chip placement via reinforcement learning: late breaking results. In Proc. 59th ACM/IEEE Design Automation Conference 1392–1393 (ACM, 2022)."/> <meta name="citation_reference" content="Yan, B. et al. Learning to floorplan like human experts via reinforcement learning. In Proc. 2024 Design Automation & Test in Europe Conference & Exhibition 1–2 (IEEE, 2024)."/> <meta name="citation_reference" content="Synopsys. What is AI chip design? https://www.synopsys.com/ai/what-is-ai-chip-design.html (accessed 23 April 2024)."/> <meta name="citation_reference" content="Cadence. Reinforcement learning. https://www.cadence.com/en_US/home/explore/reinforcement-learning.html (accessed 23 April 2024)."/> <meta name="citation_reference" content="Chuang, J. & Gil, P. Boost chip design with AI: how Synopsys DSO.ai on AWS delivers lower power and faster time-to-market. AWS Partner Network Blog https://aws.amazon.com/blogs/apn/boost-chip-design-with-ai-how-synopsys-dso-ai-on-aws-delivers-lower-power-and-faster-time-to-market (19 March 2024)."/> <meta name="citation_reference" content="Cutress, I. Cadence Cerebrus to enable chip design with ML: PPA optimization in hours, not months. AnandTech https://www.anandtech.com/show/16836/cadence-cerebrus-to-enable-chip-design-with-ml-ppa-optimization-in-hours-not-months (22 July 2021)."/> <meta name="citation_reference" content="Freund, K. AI is reshaping chip design. But where will it end? Forbes https://www.forbes.com/sites/karlfreund/2023/12/19/ai-is-reshaping-chip-design-but-where-will-it-end/?sh=3b236d65bed3 (19 December 2023)."/> <meta name="citation_reference" content="Ward-Foxton, S. AI-powered chip design goes mainstream. EETimes https://www.eetimes.com/ai-powered-chip-design-goes-mainstream/ (10 February 2023)."/> <meta name="citation_reference" content="Caballar, R. D. Q&A: Here’s how AI will change chip design. IEEE Spectrum https://spectrum.ieee.org/ai-chip-design-matlab?utm_campaign=post-teaser&utm_content=t3h9yzw5 (8 February 2022)."/> <meta name="citation_reference" content="Metcalfe, R. Machine Learning-Driven Full-Flow Chip Design Automation https://www.cadence.com/content/dam/cadence-www/global/en_US/documents/tools/digital-design-signoff/cerebrus-wp.pdf (Cadence, 2022)."/> <meta name="citation_reference" content="Sutton, R. The Bitter Lesson https://www.cs.utexas.edu/~eunsol/courses/data/bitter_lesson.pdf (13 March 2019)."/> <meta name="citation_reference" content="Yue, S. et al. Scalability and generalization of circuit training for chip floorplanning. In Proc. 2022 International Symposium on Physical Design 65–70 (2022)."/> <meta name="citation_reference" content="Gemini Team Google. Gemini: a family of highly capable multimodal models. Preprint at https://doi.org/10.48550/arXiv.2312.11805 (2023)."/> <meta name="citation_reference" content="OpenAI et al. GPT-4 technical report. Preprint at https://doi.org/10.48550/arXiv.2303.08774 (2023)."/> <meta name="citation_reference" content="Guadarrama, S. et al. Circuit Training: an open-source framework for generating chip floor plans with distributed deep reinforcement learning. GitHub https://github.com/google-research/circuit_training (2021)."/> <meta name="citation_reference" content="Jiang, J. W. et al. Pre-trained model checkpoint. GitHub https://github.com/google-research/circuit_training/?tab=readme-ov-file#PreTrainedModelCheckpoint (2021)."/> <meta name="citation_reference" content="Guadarrama, S. et al. Pre-training. GitHub https://github.com/google-research/circuit_training/blob/main/docs/PRETRAINING.md (2021)."/> <meta name="citation_reference" content="Aggarwal, C. C. Practical issues in neural network training. In Neural Networks and Deep Learning Ch. 1.4 (Springer International Publishing, 2018)."/> <meta name="citation_reference" content="Synopsys. What is physical synthesis? https://www.synopsys.com/glossary/what-is-physical-synthesis.html (accessed 23 April 2024)."/> <meta name="citation_reference" content="Karypis, G. & Kumar, V. Hmetis: a hypergraph partitioning package http://glaros.dtc.umn.edu/gkhome/metis/hmetis/overview (1998)."/> <meta name="citation_reference" content="hMETIS – hypergraph and circuit partitioning manual http://glaros.dtc.umn.edu/gkhome/metis/hmetis/download ."/> <meta name="citation_reference" content="Pan, D. Z., Liebmann, L., Yu, B., Xu, X. & Lin, Y. Pushing multiple patterning in sub-10nm: are we ready? In Proc. 52nd Annual Design Automation Conference 1–6 (ACM, 2015)."/> <meta name="citation_reference" content="Hsu, M.-K., Chang, Y.-W. & Balabanov, V. TSV-aware analytical placement for 3D IC designs. In Proc. 48th Annual Design Automation Conference 664–669 (ACM, 2011)."/> <meta name="citation_reference" content="Dean, J. Exciting directions in systems for machine learning. MLSys https://mlsys.org/virtual/2024/invited-talk/2592 (2024)."/> <meta name="citation_reference" content="Lee, J.-W. et al. A learning-based algorithm for early floorplan with flexible blocks. In 2022 IEEE Asian Solid-State Circuits Conference 1–2 (IEEE, 2022)."/> <meta name="citation_reference" content="Dean, J. Keynote: The potential of machine learning for hardware design. YouTube https://youtu.be/FraDFZ2t__A?si=skUirAfOyYH_gfqi (2022)."/> <meta name="citation_author" content="Goldie, Anna"/> <meta name="citation_author_institution" content="Google Research, Brain Team, Google, Mountain View, USA"/> <meta name="citation_author_institution" content="Computer Science Department, Stanford University, Stanford, USA"/> <meta name="citation_author" content="Mirhoseini, Azalia"/> <meta name="citation_author_institution" content="Google Research, Brain Team, Google, Mountain View, USA"/> <meta name="citation_author_institution" content="Computer Science Department, Stanford University, Stanford, USA"/> <meta name="citation_author" content="Yazgan, Mustafa"/> <meta name="citation_author_institution" content="Google Chip Implementation and Infrastructure (CI2) Team, Google, Sunnyvale, USA"/> <meta name="citation_author" content="Jiang, Joe Wenjie"/> <meta name="citation_author_institution" content="Google Research, Brain Team, Google, Mountain View, USA"/> <meta name="citation_author" content="Songhori, Ebrahim"/> <meta name="citation_author_institution" content="Google Research, Brain Team, Google, Mountain View, USA"/> <meta name="citation_author" content="Wang, Shen"/> <meta name="citation_author_institution" content="Google Research, Brain Team, Google, Mountain View, USA"/> <meta name="citation_author" content="Lee, Young-Joon"/> <meta name="citation_author_institution" content="Google Chip Implementation and Infrastructure (CI2) Team, Google, Sunnyvale, USA"/> <meta name="citation_author" content="Johnson, Eric"/> <meta name="citation_author_institution" content="Google Research, Brain Team, Google, Mountain View, USA"/> <meta name="citation_author" content="Pathak, Omkar"/> <meta name="citation_author_institution" content="Google Chip Implementation and Infrastructure (CI2) Team, Google, Sunnyvale, USA"/> <meta name="citation_author" content="Nova, Azade"/> <meta name="citation_author_institution" content="Google Research, Brain Team, Google, Mountain View, USA"/> <meta name="citation_author" content="Pak, Jiwoo"/> <meta name="citation_author_institution" content="Google Chip Implementation and Infrastructure (CI2) Team, Google, Sunnyvale, USA"/> <meta name="citation_author" content="Tong, Andy"/> <meta name="citation_author_institution" content="Google Chip Implementation and Infrastructure (CI2) Team, Google, Sunnyvale, USA"/> <meta name="citation_author" content="Srinivasa, Kavya"/> <meta name="citation_author_institution" content="Google Chip Implementation and Infrastructure (CI2) Team, Google, Sunnyvale, USA"/> <meta name="citation_author" content="Hang, William"/> <meta name="citation_author_institution" content="Computer Science Department, Stanford University, Stanford, USA"/> <meta name="citation_author" content="Tuncer, Emre"/> <meta name="citation_author_institution" content="Google Chip Implementation and Infrastructure (CI2) Team, Google, Sunnyvale, USA"/> <meta name="citation_author" content="Le, Quoc V."/> <meta name="citation_author_institution" content="Google Research, Brain Team, Google, Mountain View, USA"/> <meta name="citation_author" content="Laudon, James"/> <meta name="citation_author_institution" content="Google Research, Brain Team, Google, Mountain View, USA"/> <meta name="citation_author" content="Ho, Richard"/> <meta name="citation_author_institution" content="Google Chip Implementation and Infrastructure (CI2) Team, Google, Sunnyvale, USA"/> <meta name="citation_author" content="Carpenter, Roger"/> <meta name="citation_author_institution" content="Google Chip Implementation and Infrastructure (CI2) Team, Google, Sunnyvale, USA"/> <meta name="citation_author" content="Dean, Jeff"/> <meta name="citation_author_institution" content="Google Research, Brain Team, Google, Mountain View, USA"/> <meta name="access_endpoint" content="https://www.nature.com/platform/readcube-access"/> <meta name="twitter:site" content="@nature"/> <meta name="twitter:card" content="summary"/> <meta name="twitter:title" content="Addendum: A graph placement methodology for fast chip design"/> <meta name="twitter:description" content="Nature - Addendum: A graph placement methodology for fast chip design"/> <meta property="og:url" content="https://www.nature.com/articles/s41586-024-08032-5"/> <meta property="og:type" content="article"/> <meta property="og:site_name" content="Nature"/> <meta property="og:title" content="Addendum: A graph placement methodology for fast chip design - Nature"/> <script> window.eligibleForRa21 = 'true'; </script> </head> <body class="article-page"> <noscript><iframe src="https://www.googletagmanager.com/ns.html?id=GTM-MRVXSHQ" height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript> <div class="position-relative cleared z-index-50 background-white" data-test="top-containers"> <a class="c-skip-link" href="#content">Skip to main content</a> <div class="c-grade-c-banner u-hide"> <div class="c-grade-c-banner__container"> <p>Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.</p> </div> </div> <div class="u-hide u-show-following-ad"></div> <aside class="c-ad c-ad--728x90"> <div class="c-ad__inner" data-container-type="banner-advert"> <p class="c-ad__label">Advertisement</p> <div id="div-gpt-ad-top-1" class="div-gpt-ad advert leaderboard js-ad text-center hide-print grade-c-hide" data-ad-type="top" data-test="top-ad" data-pa11y-ignore data-gpt data-gpt-unitpath="/285/nature.com/article" data-gpt-sizes="728x90" data-gpt-targeting="type=article;pos=top;artid=s41586-024-08032-5;doi=10.1038/s41586-024-08032-5;techmeta=119;subjmeta=1042,166,639,705,987;kwrd=Computational+science,Electrical+and+electronic+engineering"> <noscript> <a href="//pubads.g.doubleclick.net/gampad/jump?iu=/285/nature.com/article&sz=728x90&c=-747431689&t=pos%3Dtop%26type%3Darticle%26artid%3Ds41586-024-08032-5%26doi%3D10.1038/s41586-024-08032-5%26techmeta%3D119%26subjmeta%3D1042,166,639,705,987%26kwrd%3DComputational+science,Electrical+and+electronic+engineering"> <img data-test="gpt-advert-fallback-img" src="//pubads.g.doubleclick.net/gampad/ad?iu=/285/nature.com/article&sz=728x90&c=-747431689&t=pos%3Dtop%26type%3Darticle%26artid%3Ds41586-024-08032-5%26doi%3D10.1038/s41586-024-08032-5%26techmeta%3D119%26subjmeta%3D1042,166,639,705,987%26kwrd%3DComputational+science,Electrical+and+electronic+engineering" alt="Advertisement" width="728" height="90"></a> </noscript> </div> </div> </aside> <header class="c-header" id="header" data-header data-track-component="nature-150-split-header" style="border-color:#000"> <div class="c-header__row"> <div class="c-header__container"> <div class="c-header__split"> <div class="c-header__logo-container"> <a href="/" data-track="click" data-track-action="home" data-track-label="image"> <picture class="c-header__logo"> <source srcset="https://media.springernature.com/full/nature-cms/uploads/product/nature/header-86f1267ea01eccd46b530284be10585e.svg" media="(min-width: 875px)"> <img src="https://media.springernature.com/full/nature-cms/uploads/product/nature/header-86f1267ea01eccd46b530284be10585e.svg" height="32" alt="Nature"> </picture> </a> </div> <ul class="c-header__menu c-header__menu--global"> <li class="c-header__item c-header__item--padding c-header__item--hide-md-max"> <a class="c-header__link" href="https://www.nature.com/siteindex" data-test="siteindex-link" data-track="click" data-track-action="open nature research index" data-track-label="link"> <span>View all journals</span> </a> </li> <li class="c-header__item c-header__item--padding c-header__item--pipe"> <a class="c-header__link c-header__link--search" href="#search-menu" data-header-expander data-test="search-link" data-track="click" data-track-action="open search tray" data-track-label="button"> <svg role="img" aria-hidden="true" focusable="false" height="22" width="22" viewBox="0 0 18 18" xmlns="http://www.w3.org/2000/svg"><path d="M16.48 15.455c.283.282.29.749.007 1.032a.738.738 0 01-1.032-.007l-3.045-3.044a7 7 0 111.026-1.026zM8 14A6 6 0 108 2a6 6 0 000 12z"/></svg><span>Search</span> </a> </li> <li class="c-header__item c-header__item--padding c-header__item--snid-account-widget c-header__item--pipe"> <a class="c-header__link eds-c-header__link" id="identity-account-widget" href='https://idp.nature.com/auth/personal/springernature?redirect_uri=https://www.nature.com/articles/s41586-024-08032-5?error=cookies_not_supported&code=e60a5aa5-04e2-40b2-8d76-bc7bcfd59e1a'><span class="eds-c-header__widget-fragment-title">Log in</span></a> </li> </ul> </div> </div> </div> <div class="c-header__row"> <div class="c-header__container" data-test="navigation-row"> <div class="c-header__split"> <ul class="c-header__menu c-header__menu--journal"> <li class="c-header__item c-header__item--dropdown-menu" data-test="explore-content-button"> <a href="#explore" class="c-header__link" data-header-expander data-test="menu-button--explore" data-track="click" data-track-action="open explore expander" data-track-label="button"> <span><span class="c-header__show-text">Explore</span> content</span><svg role="img" aria-hidden="true" focusable="false" height="16" viewBox="0 0 16 16" width="16" xmlns="http://www.w3.org/2000/svg"><path d="m5.58578644 3-3.29289322-3.29289322c-.39052429-.39052429-.39052429-1.02368927 0-1.41421356s1.02368927-.39052429 1.41421356 0l4 4c.39052429.39052429.39052429 1.02368927 0 1.41421356l-4 4c-.39052429.39052429-1.02368927.39052429-1.41421356 0s-.39052429-1.02368927 0-1.41421356z" transform="matrix(0 1 -1 0 11 3)"/></svg> </a> </li> <li class="c-header__item c-header__item--dropdown-menu"> <a href="#about-the-journal" class="c-header__link" data-header-expander data-test="menu-button--about-the-journal" data-track="click" data-track-action="open about the journal expander" data-track-label="button"> <span>About <span class="c-header__show-text">the journal</span></span><svg role="img" aria-hidden="true" focusable="false" height="16" viewBox="0 0 16 16" width="16" xmlns="http://www.w3.org/2000/svg"><path d="m5.58578644 3-3.29289322-3.29289322c-.39052429-.39052429-.39052429-1.02368927 0-1.41421356s1.02368927-.39052429 1.41421356 0l4 4c.39052429.39052429.39052429 1.02368927 0 1.41421356l-4 4c-.39052429.39052429-1.02368927.39052429-1.41421356 0s-.39052429-1.02368927 0-1.41421356z" transform="matrix(0 1 -1 0 11 3)"/></svg> </a> </li> <li class="c-header__item c-header__item--dropdown-menu" data-test="publish-with-us-button"> <a href="#publish-with-us" class="c-header__link c-header__link--dropdown-menu" data-header-expander data-test="menu-button--publish" data-track="click" data-track-action="open publish with us expander" data-track-label="button"> <span>Publish <span class="c-header__show-text">with us</span></span><svg role="img" aria-hidden="true" focusable="false" height="16" viewBox="0 0 16 16" width="16" xmlns="http://www.w3.org/2000/svg"><path d="m5.58578644 3-3.29289322-3.29289322c-.39052429-.39052429-.39052429-1.02368927 0-1.41421356s1.02368927-.39052429 1.41421356 0l4 4c.39052429.39052429.39052429 1.02368927 0 1.41421356l-4 4c-.39052429.39052429-1.02368927.39052429-1.41421356 0s-.39052429-1.02368927 0-1.41421356z" transform="matrix(0 1 -1 0 11 3)"/></svg> </a> </li> </ul> <ul class="c-header__menu c-header__menu--hide-lg-max"> <li class="c-header__item"> <a class="c-header__link" href="https://idp.nature.com/auth/personal/springernature?redirect_uri=https%3A%2F%2Fwww.nature.com%2Fmy-account%2Falerts%2Fsubscribe-journal%3Flist-id%3D1%26journal-link%3Dhttps%253A%252F%252Fwww.nature.com%252Fnature%252F" rel="nofollow" data-track="click" data-track-action="Sign up for alerts" data-track-label="link (desktop site header)" data-track-external> <span>Sign up for alerts</span><svg role="img" aria-hidden="true" focusable="false" height="18" viewBox="0 0 18 18" width="18" xmlns="http://www.w3.org/2000/svg"><path d="m4 10h2.5c.27614237 0 .5.2238576.5.5s-.22385763.5-.5.5h-3.08578644l-1.12132034 1.1213203c-.18753638.1875364-.29289322.4418903-.29289322.7071068v.1715729h14v-.1715729c0-.2652165-.1053568-.5195704-.2928932-.7071068l-1.7071068-1.7071067v-3.4142136c0-2.76142375-2.2385763-5-5-5-2.76142375 0-5 2.23857625-5 5zm3 4c0 1.1045695.8954305 2 2 2s2-.8954305 2-2zm-5 0c-.55228475 0-1-.4477153-1-1v-.1715729c0-.530433.21071368-1.0391408.58578644-1.4142135l1.41421356-1.4142136v-3c0-3.3137085 2.6862915-6 6-6s6 2.6862915 6 6v3l1.4142136 1.4142136c.3750727.3750727.5857864.8837805.5857864 1.4142135v.1715729c0 .5522847-.4477153 1-1 1h-4c0 1.6568542-1.3431458 3-3 3-1.65685425 0-3-1.3431458-3-3z" fill="#222"/></svg> </a> </li> <li class="c-header__item c-header__item--pipe"> <a class="c-header__link" href="https://www.nature.com/nature.rss" data-track="click" data-track-action="rss feed" data-track-label="link"> <span>RSS feed</span> </a> </li> </ul> </div> </div> </div> </header> <nav class="u-mb-16" aria-label="breadcrumbs"> <div class="u-container"> <ol class="c-breadcrumbs" itemscope itemtype="https://schema.org/BreadcrumbList"> <li class="c-breadcrumbs__item" id="breadcrumb0" itemprop="itemListElement" itemscope itemtype="https://schema.org/ListItem"><a class="c-breadcrumbs__link" href="/" itemprop="item" data-track="click" data-track-action="breadcrumb" data-track-category="header" data-track-label="link:nature"><span itemprop="name">nature</span></a><meta itemprop="position" content="1"> <svg class="c-breadcrumbs__chevron" role="img" aria-hidden="true" focusable="false" height="10" viewBox="0 0 10 10" width="10" xmlns="http://www.w3.org/2000/svg"> <path d="m5.96738168 4.70639573 2.39518594-2.41447274c.37913917-.38219212.98637524-.38972225 1.35419292-.01894278.37750606.38054586.37784436.99719163-.00013556 1.37821513l-4.03074001 4.06319683c-.37758093.38062133-.98937525.38100976-1.367372-.00003075l-4.03091981-4.06337806c-.37759778-.38063832-.38381821-.99150444-.01600053-1.3622839.37750607-.38054587.98772445-.38240057 1.37006824.00302197l2.39538588 2.4146743.96295325.98624457z" fill="#666" fill-rule="evenodd" transform="matrix(0 -1 1 0 0 10)"/> </svg> </li><li class="c-breadcrumbs__item" id="breadcrumb1" itemprop="itemListElement" itemscope itemtype="https://schema.org/ListItem"><a class="c-breadcrumbs__link" href="/nature/articles?type=addendum" itemprop="item" data-track="click" data-track-action="breadcrumb" data-track-category="header" data-track-label="link:addenda"><span itemprop="name">addenda</span></a><meta itemprop="position" content="2"> <svg class="c-breadcrumbs__chevron" role="img" aria-hidden="true" focusable="false" height="10" viewBox="0 0 10 10" width="10" xmlns="http://www.w3.org/2000/svg"> <path d="m5.96738168 4.70639573 2.39518594-2.41447274c.37913917-.38219212.98637524-.38972225 1.35419292-.01894278.37750606.38054586.37784436.99719163-.00013556 1.37821513l-4.03074001 4.06319683c-.37758093.38062133-.98937525.38100976-1.367372-.00003075l-4.03091981-4.06337806c-.37759778-.38063832-.38381821-.99150444-.01600053-1.3622839.37750607-.38054587.98772445-.38240057 1.37006824.00302197l2.39538588 2.4146743.96295325.98624457z" fill="#666" fill-rule="evenodd" transform="matrix(0 -1 1 0 0 10)"/> </svg> </li><li class="c-breadcrumbs__item" id="breadcrumb2" itemprop="itemListElement" itemscope itemtype="https://schema.org/ListItem"> <span itemprop="name">article</span><meta itemprop="position" content="3"></li> </ol> </div> </nav> </div> <div class="u-container u-mt-32 u-mb-32 u-clearfix" id="content" data-component="article-container" data-container-type="article"> <main class="c-article-main-column u-float-left js-main-column" data-track-component="article body"> <div class="c-context-bar u-hide" data-test="context-bar" data-context-bar aria-hidden="true"> <div class="c-context-bar__container u-container" data-track-context="sticky banner"> <div class="c-context-bar__title"> Addendum: A graph placement methodology for fast chip design </div> <div class="c-pdf-download u-clear-both js-pdf-download"> <a href="/articles/s41586-024-08032-5.pdf" class="u-button u-button--full-width u-button--primary u-justify-content-space-between c-pdf-download__link" data-article-pdf="true" data-readcube-pdf-url="true" data-test="download-pdf" data-draft-ignore="true" data-track="content_download" data-track-type="article pdf download" data-track-action="download pdf" data-track-label="link" data-track-external download> <span class="c-pdf-download__text">Download PDF</span> <svg aria-hidden="true" focusable="false" width="16" height="16" class="u-icon"><use xlink:href="#icon-download"/></svg> </a> </div> </div> </div> <article lang="en"> <div class="c-article-header"> <header> <ul class="c-article-identifiers" data-test="article-identifier"> <li class="c-article-identifiers__item" data-test="article-category">Addendum</li> <li class="c-article-identifiers__item">Published: <time datetime="2024-09-26">26 September 2024</time></li> </ul> <h1 class="c-article-title" data-test="article-title" data-article-title="">Addendum: A graph placement methodology for fast chip design</h1> <ul class="c-article-author-list c-article-author-list--short" data-test="authors-list" data-component-authors-activator="authors-list"><li class="c-article-author-list__item"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Anna-Goldie-Aff1-Aff3" data-author-popup="auth-Anna-Goldie-Aff1-Aff3" data-author-search="Goldie, Anna" data-corresp-id="c1">Anna Goldie<svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-mail-medium"></use></svg></a><span class="u-js-hide"> <a class="js-orcid" href="http://orcid.org/0000-0002-4887-6293"><span class="u-visually-hidden">ORCID: </span>orcid.org/0000-0002-4887-6293</a></span><sup class="u-js-hide"><a href="#Aff1">1</a>,<a href="#Aff3">3</a></sup><sup class="u-js-hide"> <a href="#na1">na1</a></sup>, </li><li class="c-article-author-list__item"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Azalia-Mirhoseini-Aff1-Aff3" data-author-popup="auth-Azalia-Mirhoseini-Aff1-Aff3" data-author-search="Mirhoseini, Azalia" data-corresp-id="c2">Azalia Mirhoseini<svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-mail-medium"></use></svg></a><span class="u-js-hide"> <a class="js-orcid" href="http://orcid.org/0000-0002-2440-0944"><span class="u-visually-hidden">ORCID: </span>orcid.org/0000-0002-2440-0944</a></span><sup class="u-js-hide"><a href="#Aff1">1</a>,<a href="#Aff3">3</a></sup><sup class="u-js-hide"> <a href="#na1">na1</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Mustafa-Yazgan-Aff2" data-author-popup="auth-Mustafa-Yazgan-Aff2" data-author-search="Yazgan, Mustafa">Mustafa Yazgan</a><sup class="u-js-hide"><a href="#Aff2">2</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Joe_Wenjie-Jiang-Aff1" data-author-popup="auth-Joe_Wenjie-Jiang-Aff1" data-author-search="Jiang, Joe Wenjie">Joe Wenjie Jiang</a><sup class="u-js-hide"><a href="#Aff1">1</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Ebrahim-Songhori-Aff1" data-author-popup="auth-Ebrahim-Songhori-Aff1" data-author-search="Songhori, Ebrahim">Ebrahim Songhori</a><sup class="u-js-hide"><a href="#Aff1">1</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Shen-Wang-Aff1" data-author-popup="auth-Shen-Wang-Aff1" data-author-search="Wang, Shen">Shen Wang</a><sup class="u-js-hide"><a href="#Aff1">1</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Young_Joon-Lee-Aff2" data-author-popup="auth-Young_Joon-Lee-Aff2" data-author-search="Lee, Young-Joon">Young-Joon Lee</a><sup class="u-js-hide"><a href="#Aff2">2</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Eric-Johnson-Aff1" data-author-popup="auth-Eric-Johnson-Aff1" data-author-search="Johnson, Eric">Eric Johnson</a><sup class="u-js-hide"><a href="#Aff1">1</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Omkar-Pathak-Aff2" data-author-popup="auth-Omkar-Pathak-Aff2" data-author-search="Pathak, Omkar">Omkar Pathak</a><sup class="u-js-hide"><a href="#Aff2">2</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Azade-Nova-Aff1" data-author-popup="auth-Azade-Nova-Aff1" data-author-search="Nova, Azade">Azade Nova</a><sup class="u-js-hide"><a href="#Aff1">1</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Jiwoo-Pak-Aff2" data-author-popup="auth-Jiwoo-Pak-Aff2" data-author-search="Pak, Jiwoo">Jiwoo Pak</a><sup class="u-js-hide"><a href="#Aff2">2</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Andy-Tong-Aff2" data-author-popup="auth-Andy-Tong-Aff2" data-author-search="Tong, Andy">Andy Tong</a><sup class="u-js-hide"><a href="#Aff2">2</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Kavya-Srinivasa-Aff2" data-author-popup="auth-Kavya-Srinivasa-Aff2" data-author-search="Srinivasa, Kavya">Kavya Srinivasa</a><sup class="u-js-hide"><a href="#Aff2">2</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-William-Hang-Aff3" data-author-popup="auth-William-Hang-Aff3" data-author-search="Hang, William">William Hang</a><sup class="u-js-hide"><a href="#Aff3">3</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Emre-Tuncer-Aff2" data-author-popup="auth-Emre-Tuncer-Aff2" data-author-search="Tuncer, Emre">Emre Tuncer</a><sup class="u-js-hide"><a href="#Aff2">2</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Quoc_V_-Le-Aff1" data-author-popup="auth-Quoc_V_-Le-Aff1" data-author-search="Le, Quoc V.">Quoc V. Le</a><sup class="u-js-hide"><a href="#Aff1">1</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-James-Laudon-Aff1" data-author-popup="auth-James-Laudon-Aff1" data-author-search="Laudon, James">James Laudon</a><span class="u-js-hide"> <a class="js-orcid" href="http://orcid.org/0000-0003-1061-1780"><span class="u-visually-hidden">ORCID: </span>orcid.org/0000-0003-1061-1780</a></span><sup class="u-js-hide"><a href="#Aff1">1</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Richard-Ho-Aff2" data-author-popup="auth-Richard-Ho-Aff2" data-author-search="Ho, Richard">Richard Ho</a><sup class="u-js-hide"><a href="#Aff2">2</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Roger-Carpenter-Aff2" data-author-popup="auth-Roger-Carpenter-Aff2" data-author-search="Carpenter, Roger">Roger Carpenter</a><sup class="u-js-hide"><a href="#Aff2">2</a></sup> & </li><li class="c-article-author-list__show-more" aria-label="Show all 20 authors for this article" title="Show all 20 authors for this article">…</li><li class="c-article-author-list__item"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Jeff-Dean-Aff1" data-author-popup="auth-Jeff-Dean-Aff1" data-author-search="Dean, Jeff">Jeff Dean</a><sup class="u-js-hide"><a href="#Aff1">1</a></sup> </li></ul><button aria-expanded="false" class="c-article-author-list__button"><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-down-medium"></use></svg><span>Show authors</span></button> <p class="c-article-info-details" data-container-section="info"> <a data-test="journal-link" href="/" data-track="click" data-track-action="journal homepage" data-track-category="article body" data-track-label="link"><i data-test="journal-title">Nature</i></a> <b data-test="journal-volume"><span class="u-visually-hidden">volume</span> 634</b>, <span class="u-visually-hidden">pages </span>E10–E11 (<span data-test="article-publication-year">2024</span>)<a href="#citeas" class="c-article-info-details__cite-as u-hide-print" data-track="click" data-track-action="cite this article" data-track-label="link">Cite this article</a> </p> <div class="c-article-metrics-bar__wrapper u-clear-both"> <ul class="c-article-metrics-bar u-list-reset"> <li class=" c-article-metrics-bar__item" data-test="access-count"> <p class="c-article-metrics-bar__count">16k <span class="c-article-metrics-bar__label">Accesses</span></p> </li> <li class="c-article-metrics-bar__item" data-test="altmetric-score"> <p class="c-article-metrics-bar__count">63 <span class="c-article-metrics-bar__label">Altmetric</span></p> </li> <li class="c-article-metrics-bar__item"> <p class="c-article-metrics-bar__details"><a href="/articles/s41586-024-08032-5/metrics" data-track="click" data-track-action="view metrics" data-track-label="link" rel="nofollow">Metrics <span class="u-visually-hidden">details</span></a></p> </li> </ul> </div> </header> <div class="u-js-hide" data-component="article-subject-links"> <h3 class="c-article__sub-heading">Subjects</h3> <ul class="c-article-subject-list"> <li class="c-article-subject-list__subject"><a href="/subjects/computational-science" data-track="click" data-track-action="view subject" data-track-label="link">Computational science</a></li><li class="c-article-subject-list__subject"><a href="/subjects/electrical-and-electronic-engineering" data-track="click" data-track-action="view subject" data-track-label="link">Electrical and electronic engineering</a></li> </ul> </div> <div class="u-mb-8 c-status-message c-status-message--boxed c-status-message--info"> <span class="c-status-message__icon"> <svg class="u-icon" width="18" height="18" aria-hidden="true" focusable="false"> <use xlink:href="#icon-eds-i-info-filled-medium"></use> </svg> </span> <p class="u-mt-0">The <a href="https://doi.org/10.1038/s41586-021-03544-w" class="relation-link" data-track="click" data-track-action="view linked article" data-track-label="link">Original Article</a> was published on 09 June 2021</p> </div> </div> <div class="c-article-body"> <noscript> <div class="c-nature-box c-nature-box--side " data-component="entitlement-box"> <p class="c-nature-box__text js-text">You have full access to this article via your institution.</p> <div class="c-pdf-download u-clear-both js-pdf-download"> <a href="/articles/s41586-024-08032-5.pdf" class="u-button u-button--full-width u-button--primary u-justify-content-space-between c-pdf-download__link" data-article-pdf="true" data-readcube-pdf-url="true" data-test="download-pdf" data-draft-ignore="true" data-track="content_download" data-track-type="article pdf download" data-track-action="download pdf" data-track-label="link" data-track-external download> <span class="c-pdf-download__text">Download PDF</span> <svg aria-hidden="true" focusable="false" width="16" height="16" class="u-icon"><use xlink:href="#icon-download"/></svg> </a> </div> </div> </noscript> <div class="js-context-bar-sticky-point-mobile" data-track-context="article body"> <div class="c-nature-box c-nature-box--side u-display-none u-hide-print" aria-hidden="true" data-component="entitlement-box" id=entitlement-box-entitled-mobile > <p class="c-nature-box__text js-text u-display-none" aria-hidden="true"></p> <div class="c-pdf-download u-clear-both js-pdf-download"> <a href="/articles/s41586-024-08032-5.pdf" class="u-button u-button--full-width u-button--primary u-justify-content-space-between c-pdf-download__link" data-article-pdf="true" data-readcube-pdf-url="true" data-test="download-pdf" data-draft-ignore="true" data-track="content_download" data-track-type="article pdf download" data-track-action="download pdf" data-track-label="link" data-track-external download> <span class="c-pdf-download__text">Download PDF</span> <svg aria-hidden="true" focusable="false" width="16" height="16" class="u-icon"><use xlink:href="#icon-download"/></svg> </a> </div> </div> </div> <div class="main-content"> <div class="c-article-section__content"><p>Addendum to: <i>Nature</i> <a href="https://doi.org/10.1038/s41586-021-03544-w">https://doi.org/10.1038/s41586-021-03544-w</a> Published online 9 June 2021</p></div><div class="c-article-section__content"><p>In 2020, we introduced a deep reinforcement learning method capable of generating superhuman chip layouts<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 1" title="Mirhoseini, A. & Goldie, A. et al. Chip placement with deep reinforcement learning. Preprint at 
 https://doi.org/10.48550/arXiv.2004.10746
 
 (2020)." href="/articles/s41586-024-08032-5#ref-CR1" id="ref-link-section-d82033665e531">1</a></sup>. Today, we give this method a name: AlphaChip.</p></div><div class="c-article-section__content"><p>AlphaChip was one of the first RL methods deployed to solve a real-world engineering problem, and its publication triggered an explosion of work on AI for chip design<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Lu, Y. C. et al. RL-CCD: concurrent clock and data optimization using attention-based self-supervised reinforcement learning. In Proc. 60th ACM/IEEE Design Automation Conference 1–6 (IEEE, 2023)." href="#ref-CR2" id="ref-link-section-d82033665e538">2</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Lai, Y. et al. Chipformer: transferable chip placement via offline decision transformer. In Proc. 40th International Conference on Machine Learning 18319–18345 (JMLR.org, 2023)." href="#ref-CR3" id="ref-link-section-d82033665e538_1">3</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Shi, Y., Xue, K., Song, L. & Qian, C. Macro placement by wire-mask-guided black-box optimization. In Proc. 37th International Conference on Neural Information Processing Systems 6825–6843 (Curran Associates, 2024)." href="#ref-CR4" id="ref-link-section-d82033665e538_2">4</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Lai, Y., Yao, M. & Ping, L. Maskplace: fast chip placement via reinforced visual representation learning. In Proc. 36th International Conference on Neural Information Processing Systems 24019–24030 (Curran Associates, 2024)." href="#ref-CR5" id="ref-link-section-d82033665e538_3">5</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Cheng, R. & Yan, J. On joint learning for solving placement and routing in chip design. In Proc. 35th International Conference on Neural Information Processing Systems 16508–16519 (Curran Associates, 2024)." href="#ref-CR6" id="ref-link-section-d82033665e538_4">6</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Chang, F.-C. et al. Flexible chip placement via reinforcement learning: late breaking results. In Proc. 59th ACM/IEEE Design Automation Conference 1392–1393 (ACM, 2022)." href="#ref-CR7" id="ref-link-section-d82033665e538_5">7</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Yan, B. et al. Learning to floorplan like human experts via reinforcement learning. In Proc. 2024 Design Automation & Test in Europe Conference & Exhibition 1–2 (IEEE, 2024)." href="#ref-CR8" id="ref-link-section-d82033665e538_6">8</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Synopsys. What is AI chip design? 
 https://www.synopsys.com/ai/what-is-ai-chip-design.html
 
 (accessed 23 April 2024)." href="#ref-CR9" id="ref-link-section-d82033665e538_7">9</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Cadence. Reinforcement learning. 
 https://www.cadence.com/en_US/home/explore/reinforcement-learning.html
 
 (accessed 23 April 2024)." href="#ref-CR10" id="ref-link-section-d82033665e538_8">10</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Chuang, J. & Gil, P. Boost chip design with AI: how Synopsys DSO.ai on AWS delivers lower power and faster time-to-market. AWS Partner Network Blog 
 https://aws.amazon.com/blogs/apn/boost-chip-design-with-ai-how-synopsys-dso-ai-on-aws-delivers-lower-power-and-faster-time-to-market
 
 (19 March 2024)." href="#ref-CR11" id="ref-link-section-d82033665e538_9">11</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Cutress, I. Cadence Cerebrus to enable chip design with ML: PPA optimization in hours, not months. AnandTech 
 https://www.anandtech.com/show/16836/cadence-cerebrus-to-enable-chip-design-with-ml-ppa-optimization-in-hours-not-months
 
 (22 July 2021)." href="#ref-CR12" id="ref-link-section-d82033665e538_10">12</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Freund, K. AI is reshaping chip design. But where will it end? Forbes 
 https://www.forbes.com/sites/karlfreund/2023/12/19/ai-is-reshaping-chip-design-but-where-will-it-end/?sh=3b236d65bed3
 
 (19 December 2023)." href="#ref-CR13" id="ref-link-section-d82033665e538_11">13</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Ward-Foxton, S. AI-powered chip design goes mainstream. EETimes 
 https://www.eetimes.com/ai-powered-chip-design-goes-mainstream/
 
 (10 February 2023)." href="#ref-CR14" id="ref-link-section-d82033665e538_12">14</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Caballar, R. D. Q&A: Here’s how AI will change chip design. IEEE Spectrum 
 https://spectrum.ieee.org/ai-chip-design-matlab?utm_campaign=post-teaser&utm_content=t3h9yzw5
 
 (8 February 2022)." href="#ref-CR15" id="ref-link-section-d82033665e538_13">15</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 16" title="Metcalfe, R. Machine Learning-Driven Full-Flow Chip Design Automation 
 https://www.cadence.com/content/dam/cadence-www/global/en_US/documents/tools/digital-design-signoff/cerebrus-wp.pdf
 
 (Cadence, 2022)." href="/articles/s41586-024-08032-5#ref-CR16" id="ref-link-section-d82033665e541">16</a></sup>. Nevertheless, as described in Sutton’s <i>The Bitter Lesson</i><sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 17" title="Sutton, R. The Bitter Lesson 
 https://www.cs.utexas.edu/~eunsol/courses/data/bitter_lesson.pdf
 
 (13 March 2019)." href="/articles/s41586-024-08032-5#ref-CR17" id="ref-link-section-d82033665e547">17</a></sup>, there is often reluctance to accept the application of machine learning to new areas, and ultimately this has led to some confusion around our work, which we address below. At the end of this addendum, we provide examples of high-impact deployments for the interested reader.</p></div><section data-title="Pre-training"><div class="c-article-section" id="Sec1-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec1">Pre-training</h2><div class="c-article-section__content" id="Sec1-content"><p>Unlike prior approaches, AlphaChip is a learning-based method, meaning that it becomes better and faster as it solves more instances of the chip placement problem. This pre-training significantly improves its speed, reliability, and placement quality, as discussed in the original <i>Nature</i> article and in a follow-up study at ISPD 2022<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 18" title="Yue, S. et al. Scalability and generalization of circuit training for chip floorplanning. In Proc. 2022 International Symposium on Physical Design 65–70 (2022)." href="/articles/s41586-024-08032-5#ref-CR18" id="ref-link-section-d82033665e561">18</a></sup>. Incidentally, pre-training also gives rise to the impressive capabilities of large language models like Gemini<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 19" title="Gemini Team Google. Gemini: a family of highly capable multimodal models. Preprint at 
 https://doi.org/10.48550/arXiv.2312.11805
 
 (2023)." href="/articles/s41586-024-08032-5#ref-CR19" id="ref-link-section-d82033665e565">19</a></sup> and ChatGPT<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 20" title="OpenAI et al. GPT-4 technical report. Preprint at 
 https://doi.org/10.48550/arXiv.2303.08774
 
 (2023)." href="/articles/s41586-024-08032-5#ref-CR20" id="ref-link-section-d82033665e569">20</a></sup> (the “P” stands for “pre-trained”).</p><p>Since publication, we have open-sourced a software repository<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 21" title="Guadarrama, S. et al. Circuit Training: an open-source framework for generating chip floor plans with distributed deep reinforcement learning. GitHub 
 https://github.com/google-research/circuit_training
 
 (2021)." href="/articles/s41586-024-08032-5#ref-CR21" id="ref-link-section-d82033665e576">21</a></sup> to fully reproduce the methods described in our paper. External researchers can use this repository to pre-train on a variety of chip blocks and then apply the pre-trained model to new blocks, as was done in our original paper. As part of this addendum, we are also releasing a model checkpoint pre-trained on 20 TPU blocks<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 22" title="Jiang, J. W. et al. Pre-trained model checkpoint. GitHub 
 https://github.com/google-research/circuit_training/?tab=readme-ov-file#PreTrainedModelCheckpoint
 
 (2021)." href="/articles/s41586-024-08032-5#ref-CR22" id="ref-link-section-d82033665e580">22</a></sup>. For best results, however, we continue to recommend that developers pre-train on their own in-distribution blocks<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 18" title="Yue, S. et al. Scalability and generalization of circuit training for chip floorplanning. In Proc. 2022 International Symposium on Physical Design 65–70 (2022)." href="/articles/s41586-024-08032-5#ref-CR18" id="ref-link-section-d82033665e584">18</a></sup>, and provide a tutorial on how to perform pre-training with our open-source repository<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 23" title="Guadarrama, S. et al. Pre-training. GitHub 
 https://github.com/google-research/circuit_training/blob/main/docs/PRETRAINING.md
 
 (2021)." href="/articles/s41586-024-08032-5#ref-CR23" id="ref-link-section-d82033665e588">23</a></sup>.</p><p>Obviously, not performing any pre-training at all circumvents the learning aspects of our method by removing its ability to learn from prior experience.</p></div></div></section><section data-title="Training and computational resources"><div class="c-article-section" id="Sec2-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec2">Training and computational resources</h2><div class="c-article-section__content" id="Sec2-content"><p>As an RL agent (or any machine learning model) trains, its loss typically decreases, and eventually plateaus, representing “convergence” — the model has learned what it can about the task it is performing. Training to convergence is standard practice in machine learning, and failing to do so is likely to harm performance<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 24" title="Aggarwal, C. C. Practical issues in neural network training. In Neural Networks and Deep Learning Ch. 1.4 (Springer International Publishing, 2018)." href="/articles/s41586-024-08032-5#ref-CR24" id="ref-link-section-d82033665e603">24</a></sup>.</p><p>Performance of our method scales with computational resources applied, a property which we explored further in our ISPD 2022 paper<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 18" title="Yue, S. et al. Scalability and generalization of circuit training for chip floorplanning. In Proc. 2022 International Symposium on Physical Design 65–70 (2022)." href="/articles/s41586-024-08032-5#ref-CR18" id="ref-link-section-d82033665e610">18</a></sup>. As described in our <i>Nature</i> paper, we used 16 workers, each of which consisted of 1 GPU and 32 RL environments sharing 10 CPUs via multi-processing, when fine-tuning on a particular block. Using fewer computational resources is likely to harm performance, or require running for considerably longer to achieve the same (or worse) performance.</p></div></div></section><section data-title="Initial placement"><div class="c-article-section" id="Sec3-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec3">Initial placement</h2><div class="c-article-section__content" id="Sec3-content"><p>Prior to running the methods evaluated in our <i>Nature</i> paper, an approximate initial placement from physical synthesis, the previous step of the chip design process<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 25" title="Synopsys. What is physical synthesis? 
 https://www.synopsys.com/glossary/what-is-physical-synthesis.html
 
 (accessed 23 April 2024)." href="/articles/s41586-024-08032-5#ref-CR25" id="ref-link-section-d82033665e629">25</a></sup>, was used to resolve imbalances in the sizes of standard cell clusters from hMETIS<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 26" title="Karypis, G. & Kumar, V. Hmetis: a hypergraph partitioning package 
 http://glaros.dtc.umn.edu/gkhome/metis/hmetis/overview
 
 (1998)." href="/articles/s41586-024-08032-5#ref-CR26" id="ref-link-section-d82033665e633">26</a></sup>. The RL agent does not have access to this initial placement and does not place standard cells.</p><p>Even so, we ran an ablation study which eliminated any use of initial placement whatsoever, and observed no degradation in performance (see Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/articles/s41586-024-08032-5#Tab1">1</a>). Specifically, we skipped the cluster rebalancing step and instead reduced hMETIS’s cluster imbalance parameter to its lowest setting (UBfactor = 1), which causes hMETIS to generate more balanced clusters<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 27" title="hMETIS – hypergraph and circuit partitioning manual 
 http://glaros.dtc.umn.edu/gkhome/metis/hmetis/download
 
 ." href="/articles/s41586-024-08032-5#ref-CR27" id="ref-link-section-d82033665e643">27</a></sup>.</p><div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-1"><figure><figcaption class="c-article-table__figcaption"><b id="Tab1" data-test="table-caption">Table 1 Eliminating initial placement does not degrade performance</b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/articles/s41586-024-08032-5/tables/1" aria-label="Full size table 1"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><p>This ancillary preprocessing step has been documented and open-sourced since 10 June 2022<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 21" title="Guadarrama, S. et al. Circuit Training: an open-source framework for generating chip floor plans with distributed deep reinforcement learning. GitHub 
 https://github.com/google-research/circuit_training
 
 (2021)." href="/articles/s41586-024-08032-5#ref-CR21" id="ref-link-section-d82033665e808">21</a></sup> but appears to be unnecessary.</p></div></div></section><section data-title="Benchmarks"><div class="c-article-section" id="Sec4-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec4">Benchmarks</h2><div class="c-article-section__content" id="Sec4-content"><p>In our <i>Nature</i> paper, we report results on TPU blocks with a sub-10 nm technology node size. This technology node size is typical of modern chips, but many academic papers report results on older technology node sizes, such as 45 nm or 12 nm. Chips with older technology node sizes differ substantially from a physical design perspective (e.g., at sub-10 nm, multiple patterning is typically used<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 28" title="Pan, D. Z., Liebmann, L., Yu, B., Xu, X. & Lin, Y. Pushing multiple patterning in sub-10nm: are we ready? In Proc. 52nd Annual Design Automation Conference 1–6 (ACM, 2015)." href="/articles/s41586-024-08032-5#ref-CR28" id="ref-link-section-d82033665e823">28</a></sup>, causing routing congestion issues to emerge at lower density). Therefore, for older technology node sizes, AlphaChip may benefit from adjustment to its reward function. We welcome contributions from the community to develop better-correlated cost functions for older technology node sizes.</p></div></div></section><section data-title="Clarifications to the paper"><div class="c-article-section" id="Sec5-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec5">Clarifications to the paper</h2><div class="c-article-section__content" id="Sec5-content"><p>To further reduce confusion, we have added two clarifying sentences and two minor edits to the original paper:</p><ul class="u-list-style-bullet"> <li> <p>In the caption of Fig. 4, we specify hyperparameter settings: “Density weight was set to 0.1 and congestion weight to 0”. In our experience, we have found pre-training to be effective across all hyperparameter settings.</p> </li> <li> <p>In the Methods section on “Clustering of standard cells”, we added “After clustering with hMETIS, we rebalance cluster sizes using heuristics based on an initial placement from physical synthesis, the previous step in the chip design process”. Eliminating this step appears to have no effect on performance, as shown in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/articles/s41586-024-08032-5#Tab1">1</a>.</p> </li> <li> <p>In the description of TPU blocks, we updated “up to a few hundred” to “up to 107” and “up to 131” to reflect the number of macros in the pre-training and test sets, respectively. In any case, AlphaChip has been used in production on blocks with over 500 macros.</p> </li> <li> <p>In related work, we added a citation to ref. <sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 29" title="Hsu, M.-K., Chang, Y.-W. & Balabanov, V. TSV-aware analytical placement for 3D IC designs. In Proc. 48th Annual Design Automation Conference 664–669 (ACM, 2011)." href="/articles/s41586-024-08032-5#ref-CR29" id="ref-link-section-d82033665e862">29</a></sup> as an additional example of weighted-average in nonlinear optimization.</p> </li> </ul><p>We also wish to clarify that Anna Goldie and Azalia Mirhoseini are co-first authors of the original <i>Nature</i> article, and the order of their names was determined by a coin flip.</p></div></div></section><section data-title="Looking forward: AI methods transform the entire chip design process"><div class="c-article-section" id="Sec6-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec6">Looking forward: AI methods transform the entire chip design process</h2><div class="c-article-section__content" id="Sec6-content"><p>Since its publication in <i>Nature</i>, AlphaChip has been used in three additional generations of Google’s flagship AI accelerator, the Tensor Processing Unit (TPU). These chips have been manufactured and deployed in datacentres all over the world. The gap between the performance of AlphaChip and human experts has grown with each successive generation of TPU, going from 10 RL-placed blocks and 3.2% wirelength reduction vs. human experts in TPU v5e, to 15 blocks with 4.5% reduction in TPU v5p, to 25 blocks with 6.2% reduction in Trillium<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 30" title="Dean, J. Exciting directions in systems for machine learning. MLSys 
 https://mlsys.org/virtual/2024/invited-talk/2592
 
 (2024)." href="/articles/s41586-024-08032-5#ref-CR30" id="ref-link-section-d82033665e885">30</a></sup>. AlphaChip has also generated superhuman chip layouts for blocks used in datacentre CPUs (Axion) and other unannounced chips across Alphabet. Other organizations have adopted our approach and built on it. For example, MediaTek, a leading global chipmaker, extended AlphaChip to accelerate development of their most advanced chips, while improving power, performance, and area<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 31" title="Lee, J.-W. et al. A learning-based algorithm for early floorplan with flexible blocks. In 2022 IEEE Asian Solid-State Circuits Conference 1–2 (IEEE, 2022)." href="/articles/s41586-024-08032-5#ref-CR31" id="ref-link-section-d82033665e889">31</a></sup>.</p><p>AlphaChip is just the beginning. We envision a future in which AI methods automate the entire chip design process, dramatically accelerating the design cycle and unlocking new frontiers in performance through superhuman algorithms and end-to-end co-optimization of hardware, software, and machine learning models<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 32" title="Dean, J. Keynote: The potential of machine learning for hardware design. YouTube 
 https://youtu.be/FraDFZ2t__A?si=skUirAfOyYH_gfqi
 
 (2022)." href="/articles/s41586-024-08032-5#ref-CR32" id="ref-link-section-d82033665e896">32</a></sup>. We are excited to work together with the community to close the loop between AI for chip design and chip design for AI.</p></div></div></section> </div> <div> <div id="MagazineFulltextArticleBodySuffix"><section aria-labelledby="Bib1" data-title="References"><div class="c-article-section" id="Bib1-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Bib1">References</h2><div class="c-article-section__content" id="Bib1-content"><div data-container-section="references"><ol class="c-article-references" data-track-component="outbound reference" data-track-context="references section"><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="1."><p class="c-article-references__text" id="ref-CR1">Mirhoseini, A. & Goldie, A. et al. Chip placement with deep reinforcement learning. Preprint at <a href="https://doi.org/10.48550/arXiv.2004.10746" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.48550/arXiv.2004.10746">https://doi.org/10.48550/arXiv.2004.10746</a> (2020).</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="2."><p class="c-article-references__text" id="ref-CR2">Lu, Y. C. et al. RL-CCD: concurrent clock and data optimization using attention-based self-supervised reinforcement learning. In <i>Proc. 60th ACM/IEEE Design Automation Conference</i> 1–6 (IEEE, 2023).</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="3."><p class="c-article-references__text" id="ref-CR3">Lai, Y. et al. Chipformer: transferable chip placement via offline decision transformer. In <i>Proc. 40th International Conference on Machine Learning</i> 18319–18345 (JMLR.org, 2023).</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="4."><p class="c-article-references__text" id="ref-CR4">Shi, Y., Xue, K., Song, L. & Qian, C. Macro placement by wire-mask-guided black-box optimization. In <i>Proc. 37th International Conference on Neural Information Processing Systems</i> 6825–6843 (Curran Associates, 2024).</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="5."><p class="c-article-references__text" id="ref-CR5">Lai, Y., Yao, M. & Ping, L. Maskplace: fast chip placement via reinforced visual representation learning. In <i>Proc. 36th International Conference on Neural Information Processing Systems</i> 24019–24030 (Curran Associates, 2024).</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="6."><p class="c-article-references__text" id="ref-CR6">Cheng, R. & Yan, J. On joint learning for solving placement and routing in chip design. In <i>Proc. 35th International Conference on Neural Information Processing Systems</i> 16508–16519 (Curran Associates, 2024).</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="7."><p class="c-article-references__text" id="ref-CR7">Chang, F.-C. et al. Flexible chip placement via reinforcement learning: late breaking results. In <i>Proc. 59th ACM/IEEE Design Automation Conference</i> 1392–1393 (ACM, 2022).</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="8."><p class="c-article-references__text" id="ref-CR8">Yan, B. et al. Learning to floorplan like human experts via reinforcement learning. In <i>Proc. 2024 Design Automation & Test in Europe Conference & Exhibition</i> 1–2 (IEEE, 2024).</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="9."><p class="c-article-references__text" id="ref-CR9">Synopsys. What is AI chip design? <a href="https://www.synopsys.com/ai/what-is-ai-chip-design.html" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="https://www.synopsys.com/ai/what-is-ai-chip-design.html">https://www.synopsys.com/ai/what-is-ai-chip-design.html</a> (accessed 23 April 2024).</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="10."><p class="c-article-references__text" id="ref-CR10">Cadence. Reinforcement learning. <a href="https://www.cadence.com/en_US/home/explore/reinforcement-learning.html" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="https://www.cadence.com/en_US/home/explore/reinforcement-learning.html">https://www.cadence.com/en_US/home/explore/reinforcement-learning.html</a> (accessed 23 April 2024).</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="11."><p class="c-article-references__text" id="ref-CR11">Chuang, J. & Gil, P. Boost chip design with AI: how Synopsys DSO.ai on AWS delivers lower power and faster time-to-market. <i>AWS Partner Network Blog</i> <a href="https://aws.amazon.com/blogs/apn/boost-chip-design-with-ai-how-synopsys-dso-ai-on-aws-delivers-lower-power-and-faster-time-to-market" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="https://aws.amazon.com/blogs/apn/boost-chip-design-with-ai-how-synopsys-dso-ai-on-aws-delivers-lower-power-and-faster-time-to-market">https://aws.amazon.com/blogs/apn/boost-chip-design-with-ai-how-synopsys-dso-ai-on-aws-delivers-lower-power-and-faster-time-to-market</a> (19 March 2024).</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="12."><p class="c-article-references__text" id="ref-CR12">Cutress, I. Cadence Cerebrus to enable chip design with ML: PPA optimization in hours, not months. <i>AnandTech</i> <a href="https://www.anandtech.com/show/16836/cadence-cerebrus-to-enable-chip-design-with-ml-ppa-optimization-in-hours-not-months" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="https://www.anandtech.com/show/16836/cadence-cerebrus-to-enable-chip-design-with-ml-ppa-optimization-in-hours-not-months">https://www.anandtech.com/show/16836/cadence-cerebrus-to-enable-chip-design-with-ml-ppa-optimization-in-hours-not-months</a> (22 July 2021).</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="13."><p class="c-article-references__text" id="ref-CR13">Freund, K. AI is reshaping chip design. But where will it end? <i>Forbes</i> <a href="https://www.forbes.com/sites/karlfreund/2023/12/19/ai-is-reshaping-chip-design-but-where-will-it-end/?sh=3b236d65bed3" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="https://www.forbes.com/sites/karlfreund/2023/12/19/ai-is-reshaping-chip-design-but-where-will-it-end/?sh=3b236d65bed3">https://www.forbes.com/sites/karlfreund/2023/12/19/ai-is-reshaping-chip-design-but-where-will-it-end/?sh=3b236d65bed3</a> (19 December 2023).</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="14."><p class="c-article-references__text" id="ref-CR14">Ward-Foxton, S. AI-powered chip design goes mainstream. <i>EETimes</i> <a href="https://www.eetimes.com/ai-powered-chip-design-goes-mainstream/" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="https://www.eetimes.com/ai-powered-chip-design-goes-mainstream/">https://www.eetimes.com/ai-powered-chip-design-goes-mainstream/</a> (10 February 2023).</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="15."><p class="c-article-references__text" id="ref-CR15">Caballar, R. D. Q&A: Here’s how AI will change chip design. <i>IEEE Spectrum</i> <a href="https://spectrum.ieee.org/ai-chip-design-matlab?utm_campaign=post-teaser&utm_content=t3h9yzw5" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="https://spectrum.ieee.org/ai-chip-design-matlab?utm_campaign=post-teaser&utm_content=t3h9yzw5">https://spectrum.ieee.org/ai-chip-design-matlab?utm_campaign=post-teaser&utm_content=t3h9yzw5</a> (8 February 2022).</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="16."><p class="c-article-references__text" id="ref-CR16">Metcalfe, R. <i>Machine Learning-Driven Full-Flow Chip Design Automation</i> <a href="https://www.cadence.com/content/dam/cadence-www/global/en_US/documents/tools/digital-design-signoff/cerebrus-wp.pdf" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="https://www.cadence.com/content/dam/cadence-www/global/en_US/documents/tools/digital-design-signoff/cerebrus-wp.pdf">https://www.cadence.com/content/dam/cadence-www/global/en_US/documents/tools/digital-design-signoff/cerebrus-wp.pdf</a> (Cadence, 2022).</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="17."><p class="c-article-references__text" id="ref-CR17">Sutton, R. <i>The Bitter Lesson</i> <a href="https://www.cs.utexas.edu/~eunsol/courses/data/bitter_lesson.pdf" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="https://www.cs.utexas.edu/~eunsol/courses/data/bitter_lesson.pdf">https://www.cs.utexas.edu/~eunsol/courses/data/bitter_lesson.pdf</a> (13 March 2019).</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="18."><p class="c-article-references__text" id="ref-CR18">Yue, S. et al. Scalability and generalization of circuit training for chip floorplanning. In <i>Proc. 2022 International Symposium on Physical Design</i> 65–70 (2022).</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="19."><p class="c-article-references__text" id="ref-CR19">Gemini Team Google. Gemini: a family of highly capable multimodal models. Preprint at <a href="https://doi.org/10.48550/arXiv.2312.11805" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.48550/arXiv.2312.11805">https://doi.org/10.48550/arXiv.2312.11805</a> (2023).</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="20."><p class="c-article-references__text" id="ref-CR20">OpenAI et al. GPT-4 technical report. Preprint at <a href="https://doi.org/10.48550/arXiv.2303.08774" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.48550/arXiv.2303.08774">https://doi.org/10.48550/arXiv.2303.08774</a> (2023).</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="21."><p class="c-article-references__text" id="ref-CR21">Guadarrama, S. et al. Circuit Training: an open-source framework for generating chip floor plans with distributed deep reinforcement learning. <i>GitHub</i> <a href="https://github.com/google-research/circuit_training" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="https://github.com/google-research/circuit_training">https://github.com/google-research/circuit_training</a> (2021).</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="22."><p class="c-article-references__text" id="ref-CR22">Jiang, J. W. et al. Pre-trained model checkpoint. <i>GitHub</i> <a href="https://github.com/google-research/circuit_training/?tab=readme-ov-file#PreTrainedModelCheckpoint" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="https://github.com/google-research/circuit_training/?tab=readme-ov-file#PreTrainedModelCheckpoint">https://github.com/google-research/circuit_training/?tab=readme-ov-file#PreTrainedModelCheckpoint</a> (2021).</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="23."><p class="c-article-references__text" id="ref-CR23">Guadarrama, S. et al. Pre-training. <i>GitHub</i> <a href="https://github.com/google-research/circuit_training/blob/main/docs/PRETRAINING.md" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="https://github.com/google-research/circuit_training/blob/main/docs/PRETRAINING.md">https://github.com/google-research/circuit_training/blob/main/docs/PRETRAINING.md</a> (2021).</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="24."><p class="c-article-references__text" id="ref-CR24">Aggarwal, C. C. Practical issues in neural network training. In <i>Neural Networks and Deep Learning</i> Ch. 1.4 (Springer International Publishing, 2018).</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="25."><p class="c-article-references__text" id="ref-CR25">Synopsys. What is physical synthesis? <a href="https://www.synopsys.com/glossary/what-is-physical-synthesis.html" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="https://www.synopsys.com/glossary/what-is-physical-synthesis.html">https://www.synopsys.com/glossary/what-is-physical-synthesis.html</a> (accessed 23 April 2024).</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="26."><p class="c-article-references__text" id="ref-CR26">Karypis, G. & Kumar, V. Hmetis: a hypergraph partitioning package <a href="http://glaros.dtc.umn.edu/gkhome/metis/hmetis/overview" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://glaros.dtc.umn.edu/gkhome/metis/hmetis/overview">http://glaros.dtc.umn.edu/gkhome/metis/hmetis/overview</a> (1998).</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="27."><p class="c-article-references__text" id="ref-CR27">hMETIS – hypergraph and circuit partitioning manual <a href="http://glaros.dtc.umn.edu/gkhome/metis/hmetis/download" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://glaros.dtc.umn.edu/gkhome/metis/hmetis/download">http://glaros.dtc.umn.edu/gkhome/metis/hmetis/download</a>.</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="28."><p class="c-article-references__text" id="ref-CR28">Pan, D. Z., Liebmann, L., Yu, B., Xu, X. & Lin, Y. Pushing multiple patterning in sub-10nm: are we ready? In <i>Proc. 52nd Annual Design Automation Conference</i> 1–6 (ACM, 2015).</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="29."><p class="c-article-references__text" id="ref-CR29">Hsu, M.-K., Chang, Y.-W. & Balabanov, V. TSV-aware analytical placement for 3D IC designs. In <i>Proc. 48th Annual Design Automation Conference</i> 664–669 (ACM, 2011).</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="30."><p class="c-article-references__text" id="ref-CR30">Dean, J. Exciting directions in systems for machine learning. <i>MLSys</i> <a href="https://mlsys.org/virtual/2024/invited-talk/2592" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="https://mlsys.org/virtual/2024/invited-talk/2592">https://mlsys.org/virtual/2024/invited-talk/2592</a> (2024).</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="31."><p class="c-article-references__text" id="ref-CR31">Lee, J.-W. et al. A learning-based algorithm for early floorplan with flexible blocks. In <i>2022 IEEE Asian Solid-State Circuits Conference</i> 1–2 (IEEE, 2022).</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="32."><p class="c-article-references__text" id="ref-CR32">Dean, J. Keynote: The potential of machine learning for hardware design. <i>YouTube</i> <a href="https://youtu.be/FraDFZ2t__A?si=skUirAfOyYH_gfqi" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="https://youtu.be/FraDFZ2t__A?si=skUirAfOyYH_gfqi">https://youtu.be/FraDFZ2t__A?si=skUirAfOyYH_gfqi</a> (2022).</p></li></ol><p class="c-article-references__download u-hide-print"><a data-track="click" data-track-action="download citation references" data-track-label="link" rel="nofollow" href="https://citation-needed.springer.com/v2/references/10.1038/s41586-024-08032-5?format=refman&flavour=references">Download references<svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-download-medium"></use></svg></a></p></div></div></div></section></div><section aria-labelledby="author-information" data-title="Author information"><div class="c-article-section" id="author-information-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="author-information">Author information</h2><div class="c-article-section__content" id="author-information-content"><span class="c-article-author-information__subtitle u-visually-hidden" id="author-notes">Author notes</span><ol class="c-article-author-information__list"><li class="c-article-author-information__item" id="na1"><p>These authors contributed equally: Azalia Mirhoseini, Anna Goldie</p></li></ol><h3 class="c-article__sub-heading" id="affiliations">Authors and Affiliations</h3><ol class="c-article-author-affiliation__list"><li id="Aff1"><p class="c-article-author-affiliation__address">Google Research, Brain Team, Google, Mountain View, CA, USA</p><p class="c-article-author-affiliation__authors-list">Anna Goldie, Azalia Mirhoseini, Joe Wenjie Jiang, Ebrahim Songhori, Shen Wang, Eric Johnson, Azade Nova, Quoc V. Le, James Laudon & Jeff Dean</p></li><li id="Aff2"><p class="c-article-author-affiliation__address">Google Chip Implementation and Infrastructure (CI2) Team, Google, Sunnyvale, CA, USA</p><p class="c-article-author-affiliation__authors-list">Mustafa Yazgan, Young-Joon Lee, Omkar Pathak, Jiwoo Pak, Andy Tong, Kavya Srinivasa, Emre Tuncer, Richard Ho & Roger Carpenter</p></li><li id="Aff3"><p class="c-article-author-affiliation__address">Computer Science Department, Stanford University, Stanford, CA, USA</p><p class="c-article-author-affiliation__authors-list">Anna Goldie, Azalia Mirhoseini & William Hang</p></li></ol><div class="u-js-hide u-hide-print" data-test="author-info"><span class="c-article__sub-heading">Authors</span><ol class="c-article-authors-search u-list-reset"><li id="auth-Anna-Goldie-Aff1-Aff3"><span class="c-article-authors-search__title u-h3 js-search-name">Anna Goldie</span><div class="c-article-authors-search__list"><div class="c-article-authors-search__item c-article-authors-search__list-item--left"><a href="/search?author=Anna%20Goldie" class="c-article-button" data-track="click" data-track-action="author link - publication" data-track-label="link" rel="nofollow">View author publications</a></div><div class="c-article-authors-search__item c-article-authors-search__list-item--right"><p class="search-in-title-js c-article-authors-search__text">You can also search for this author in <span class="c-article-identifiers"><a class="c-article-identifiers__item" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=search&term=Anna%20Goldie" data-track="click" data-track-action="author link - pubmed" data-track-label="link" rel="nofollow">PubMed</a><span class="u-hide"> </span><a class="c-article-identifiers__item" href="http://scholar.google.co.uk/scholar?as_q=&num=10&btnG=Search+Scholar&as_epq=&as_oq=&as_eq=&as_occt=any&as_sauthors=%22Anna%20Goldie%22&as_publication=&as_ylo=&as_yhi=&as_allsubj=all&hl=en" data-track="click" data-track-action="author link - scholar" data-track-label="link" rel="nofollow">Google Scholar</a></span></p></div></div></li><li id="auth-Azalia-Mirhoseini-Aff1-Aff3"><span class="c-article-authors-search__title u-h3 js-search-name">Azalia Mirhoseini</span><div class="c-article-authors-search__list"><div class="c-article-authors-search__item c-article-authors-search__list-item--left"><a href="/search?author=Azalia%20Mirhoseini" class="c-article-button" data-track="click" data-track-action="author link - publication" data-track-label="link" rel="nofollow">View author publications</a></div><div class="c-article-authors-search__item c-article-authors-search__list-item--right"><p class="search-in-title-js c-article-authors-search__text">You can also search for this author in <span class="c-article-identifiers"><a class="c-article-identifiers__item" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=search&term=Azalia%20Mirhoseini" data-track="click" data-track-action="author link - pubmed" data-track-label="link" rel="nofollow">PubMed</a><span class="u-hide"> </span><a class="c-article-identifiers__item" href="http://scholar.google.co.uk/scholar?as_q=&num=10&btnG=Search+Scholar&as_epq=&as_oq=&as_eq=&as_occt=any&as_sauthors=%22Azalia%20Mirhoseini%22&as_publication=&as_ylo=&as_yhi=&as_allsubj=all&hl=en" data-track="click" data-track-action="author link - scholar" data-track-label="link" rel="nofollow">Google Scholar</a></span></p></div></div></li><li id="auth-Mustafa-Yazgan-Aff2"><span class="c-article-authors-search__title u-h3 js-search-name">Mustafa Yazgan</span><div class="c-article-authors-search__list"><div class="c-article-authors-search__item c-article-authors-search__list-item--left"><a href="/search?author=Mustafa%20Yazgan" class="c-article-button" data-track="click" data-track-action="author link - publication" data-track-label="link" rel="nofollow">View author publications</a></div><div class="c-article-authors-search__item c-article-authors-search__list-item--right"><p class="search-in-title-js c-article-authors-search__text">You can also search for this author in <span class="c-article-identifiers"><a class="c-article-identifiers__item" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=search&term=Mustafa%20Yazgan" data-track="click" data-track-action="author link - pubmed" data-track-label="link" rel="nofollow">PubMed</a><span class="u-hide"> </span><a class="c-article-identifiers__item" href="http://scholar.google.co.uk/scholar?as_q=&num=10&btnG=Search+Scholar&as_epq=&as_oq=&as_eq=&as_occt=any&as_sauthors=%22Mustafa%20Yazgan%22&as_publication=&as_ylo=&as_yhi=&as_allsubj=all&hl=en" data-track="click" data-track-action="author link - scholar" data-track-label="link" rel="nofollow">Google Scholar</a></span></p></div></div></li><li id="auth-Joe_Wenjie-Jiang-Aff1"><span class="c-article-authors-search__title u-h3 js-search-name">Joe Wenjie Jiang</span><div class="c-article-authors-search__list"><div class="c-article-authors-search__item c-article-authors-search__list-item--left"><a href="/search?author=Joe%20Wenjie%20Jiang" class="c-article-button" data-track="click" data-track-action="author link - publication" data-track-label="link" rel="nofollow">View author publications</a></div><div class="c-article-authors-search__item c-article-authors-search__list-item--right"><p class="search-in-title-js c-article-authors-search__text">You can also search for this author in <span class="c-article-identifiers"><a class="c-article-identifiers__item" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=search&term=Joe%20Wenjie%20Jiang" data-track="click" data-track-action="author link - pubmed" data-track-label="link" rel="nofollow">PubMed</a><span class="u-hide"> </span><a class="c-article-identifiers__item" href="http://scholar.google.co.uk/scholar?as_q=&num=10&btnG=Search+Scholar&as_epq=&as_oq=&as_eq=&as_occt=any&as_sauthors=%22Joe%20Wenjie%20Jiang%22&as_publication=&as_ylo=&as_yhi=&as_allsubj=all&hl=en" data-track="click" data-track-action="author link - scholar" data-track-label="link" rel="nofollow">Google Scholar</a></span></p></div></div></li><li id="auth-Ebrahim-Songhori-Aff1"><span class="c-article-authors-search__title u-h3 js-search-name">Ebrahim Songhori</span><div class="c-article-authors-search__list"><div class="c-article-authors-search__item c-article-authors-search__list-item--left"><a href="/search?author=Ebrahim%20Songhori" class="c-article-button" data-track="click" data-track-action="author link - publication" data-track-label="link" rel="nofollow">View author publications</a></div><div class="c-article-authors-search__item c-article-authors-search__list-item--right"><p class="search-in-title-js c-article-authors-search__text">You can also search for this author in <span class="c-article-identifiers"><a class="c-article-identifiers__item" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=search&term=Ebrahim%20Songhori" data-track="click" data-track-action="author link - pubmed" data-track-label="link" rel="nofollow">PubMed</a><span class="u-hide"> </span><a class="c-article-identifiers__item" href="http://scholar.google.co.uk/scholar?as_q=&num=10&btnG=Search+Scholar&as_epq=&as_oq=&as_eq=&as_occt=any&as_sauthors=%22Ebrahim%20Songhori%22&as_publication=&as_ylo=&as_yhi=&as_allsubj=all&hl=en" data-track="click" data-track-action="author link - scholar" data-track-label="link" rel="nofollow">Google Scholar</a></span></p></div></div></li><li id="auth-Shen-Wang-Aff1"><span class="c-article-authors-search__title u-h3 js-search-name">Shen Wang</span><div class="c-article-authors-search__list"><div class="c-article-authors-search__item c-article-authors-search__list-item--left"><a href="/search?author=Shen%20Wang" class="c-article-button" data-track="click" data-track-action="author link - publication" data-track-label="link" rel="nofollow">View author publications</a></div><div class="c-article-authors-search__item c-article-authors-search__list-item--right"><p class="search-in-title-js c-article-authors-search__text">You can also search for this author in <span class="c-article-identifiers"><a class="c-article-identifiers__item" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=search&term=Shen%20Wang" data-track="click" data-track-action="author link - pubmed" data-track-label="link" rel="nofollow">PubMed</a><span class="u-hide"> </span><a class="c-article-identifiers__item" href="http://scholar.google.co.uk/scholar?as_q=&num=10&btnG=Search+Scholar&as_epq=&as_oq=&as_eq=&as_occt=any&as_sauthors=%22Shen%20Wang%22&as_publication=&as_ylo=&as_yhi=&as_allsubj=all&hl=en" data-track="click" data-track-action="author link - scholar" data-track-label="link" rel="nofollow">Google Scholar</a></span></p></div></div></li><li id="auth-Young_Joon-Lee-Aff2"><span class="c-article-authors-search__title u-h3 js-search-name">Young-Joon Lee</span><div class="c-article-authors-search__list"><div class="c-article-authors-search__item c-article-authors-search__list-item--left"><a href="/search?author=Young-Joon%20Lee" class="c-article-button" data-track="click" data-track-action="author link - publication" data-track-label="link" rel="nofollow">View author publications</a></div><div class="c-article-authors-search__item c-article-authors-search__list-item--right"><p class="search-in-title-js c-article-authors-search__text">You can also search for this author in <span class="c-article-identifiers"><a class="c-article-identifiers__item" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=search&term=Young-Joon%20Lee" data-track="click" data-track-action="author link - pubmed" data-track-label="link" rel="nofollow">PubMed</a><span class="u-hide"> </span><a class="c-article-identifiers__item" href="http://scholar.google.co.uk/scholar?as_q=&num=10&btnG=Search+Scholar&as_epq=&as_oq=&as_eq=&as_occt=any&as_sauthors=%22Young-Joon%20Lee%22&as_publication=&as_ylo=&as_yhi=&as_allsubj=all&hl=en" data-track="click" data-track-action="author link - scholar" data-track-label="link" rel="nofollow">Google Scholar</a></span></p></div></div></li><li id="auth-Eric-Johnson-Aff1"><span class="c-article-authors-search__title u-h3 js-search-name">Eric Johnson</span><div class="c-article-authors-search__list"><div class="c-article-authors-search__item c-article-authors-search__list-item--left"><a href="/search?author=Eric%20Johnson" class="c-article-button" data-track="click" data-track-action="author link - publication" data-track-label="link" rel="nofollow">View author publications</a></div><div class="c-article-authors-search__item c-article-authors-search__list-item--right"><p class="search-in-title-js c-article-authors-search__text">You can also search for this author in <span class="c-article-identifiers"><a class="c-article-identifiers__item" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=search&term=Eric%20Johnson" data-track="click" data-track-action="author link - pubmed" data-track-label="link" rel="nofollow">PubMed</a><span class="u-hide"> </span><a class="c-article-identifiers__item" href="http://scholar.google.co.uk/scholar?as_q=&num=10&btnG=Search+Scholar&as_epq=&as_oq=&as_eq=&as_occt=any&as_sauthors=%22Eric%20Johnson%22&as_publication=&as_ylo=&as_yhi=&as_allsubj=all&hl=en" data-track="click" data-track-action="author link - scholar" data-track-label="link" rel="nofollow">Google Scholar</a></span></p></div></div></li><li id="auth-Omkar-Pathak-Aff2"><span class="c-article-authors-search__title u-h3 js-search-name">Omkar Pathak</span><div class="c-article-authors-search__list"><div class="c-article-authors-search__item c-article-authors-search__list-item--left"><a href="/search?author=Omkar%20Pathak" class="c-article-button" data-track="click" data-track-action="author link - publication" data-track-label="link" rel="nofollow">View author publications</a></div><div class="c-article-authors-search__item c-article-authors-search__list-item--right"><p class="search-in-title-js c-article-authors-search__text">You can also search for this author in <span class="c-article-identifiers"><a class="c-article-identifiers__item" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=search&term=Omkar%20Pathak" data-track="click" data-track-action="author link - pubmed" data-track-label="link" rel="nofollow">PubMed</a><span class="u-hide"> </span><a class="c-article-identifiers__item" href="http://scholar.google.co.uk/scholar?as_q=&num=10&btnG=Search+Scholar&as_epq=&as_oq=&as_eq=&as_occt=any&as_sauthors=%22Omkar%20Pathak%22&as_publication=&as_ylo=&as_yhi=&as_allsubj=all&hl=en" data-track="click" data-track-action="author link - scholar" data-track-label="link" rel="nofollow">Google Scholar</a></span></p></div></div></li><li id="auth-Azade-Nova-Aff1"><span class="c-article-authors-search__title u-h3 js-search-name">Azade Nova</span><div class="c-article-authors-search__list"><div class="c-article-authors-search__item c-article-authors-search__list-item--left"><a href="/search?author=Azade%20Nova" class="c-article-button" data-track="click" data-track-action="author link - publication" data-track-label="link" rel="nofollow">View author publications</a></div><div class="c-article-authors-search__item c-article-authors-search__list-item--right"><p class="search-in-title-js c-article-authors-search__text">You can also search for this author in <span class="c-article-identifiers"><a class="c-article-identifiers__item" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=search&term=Azade%20Nova" data-track="click" data-track-action="author link - pubmed" data-track-label="link" rel="nofollow">PubMed</a><span class="u-hide"> </span><a class="c-article-identifiers__item" href="http://scholar.google.co.uk/scholar?as_q=&num=10&btnG=Search+Scholar&as_epq=&as_oq=&as_eq=&as_occt=any&as_sauthors=%22Azade%20Nova%22&as_publication=&as_ylo=&as_yhi=&as_allsubj=all&hl=en" data-track="click" data-track-action="author link - scholar" data-track-label="link" rel="nofollow">Google Scholar</a></span></p></div></div></li><li id="auth-Jiwoo-Pak-Aff2"><span class="c-article-authors-search__title u-h3 js-search-name">Jiwoo Pak</span><div class="c-article-authors-search__list"><div class="c-article-authors-search__item c-article-authors-search__list-item--left"><a href="/search?author=Jiwoo%20Pak" class="c-article-button" data-track="click" data-track-action="author link - publication" data-track-label="link" rel="nofollow">View author publications</a></div><div class="c-article-authors-search__item c-article-authors-search__list-item--right"><p class="search-in-title-js c-article-authors-search__text">You can also search for this author in <span class="c-article-identifiers"><a class="c-article-identifiers__item" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=search&term=Jiwoo%20Pak" data-track="click" data-track-action="author link - pubmed" data-track-label="link" rel="nofollow">PubMed</a><span class="u-hide"> </span><a class="c-article-identifiers__item" href="http://scholar.google.co.uk/scholar?as_q=&num=10&btnG=Search+Scholar&as_epq=&as_oq=&as_eq=&as_occt=any&as_sauthors=%22Jiwoo%20Pak%22&as_publication=&as_ylo=&as_yhi=&as_allsubj=all&hl=en" data-track="click" data-track-action="author link - scholar" data-track-label="link" rel="nofollow">Google Scholar</a></span></p></div></div></li><li id="auth-Andy-Tong-Aff2"><span class="c-article-authors-search__title u-h3 js-search-name">Andy Tong</span><div class="c-article-authors-search__list"><div class="c-article-authors-search__item c-article-authors-search__list-item--left"><a href="/search?author=Andy%20Tong" class="c-article-button" data-track="click" data-track-action="author link - publication" data-track-label="link" rel="nofollow">View author publications</a></div><div class="c-article-authors-search__item c-article-authors-search__list-item--right"><p class="search-in-title-js c-article-authors-search__text">You can also search for this author in <span class="c-article-identifiers"><a class="c-article-identifiers__item" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=search&term=Andy%20Tong" data-track="click" data-track-action="author link - pubmed" data-track-label="link" rel="nofollow">PubMed</a><span class="u-hide"> </span><a class="c-article-identifiers__item" href="http://scholar.google.co.uk/scholar?as_q=&num=10&btnG=Search+Scholar&as_epq=&as_oq=&as_eq=&as_occt=any&as_sauthors=%22Andy%20Tong%22&as_publication=&as_ylo=&as_yhi=&as_allsubj=all&hl=en" data-track="click" data-track-action="author link - scholar" data-track-label="link" rel="nofollow">Google Scholar</a></span></p></div></div></li><li id="auth-Kavya-Srinivasa-Aff2"><span class="c-article-authors-search__title u-h3 js-search-name">Kavya Srinivasa</span><div class="c-article-authors-search__list"><div class="c-article-authors-search__item c-article-authors-search__list-item--left"><a href="/search?author=Kavya%20Srinivasa" class="c-article-button" data-track="click" data-track-action="author link - publication" data-track-label="link" rel="nofollow">View author publications</a></div><div class="c-article-authors-search__item c-article-authors-search__list-item--right"><p class="search-in-title-js c-article-authors-search__text">You can also search for this author in <span class="c-article-identifiers"><a class="c-article-identifiers__item" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=search&term=Kavya%20Srinivasa" data-track="click" data-track-action="author link - pubmed" data-track-label="link" rel="nofollow">PubMed</a><span class="u-hide"> </span><a class="c-article-identifiers__item" href="http://scholar.google.co.uk/scholar?as_q=&num=10&btnG=Search+Scholar&as_epq=&as_oq=&as_eq=&as_occt=any&as_sauthors=%22Kavya%20Srinivasa%22&as_publication=&as_ylo=&as_yhi=&as_allsubj=all&hl=en" data-track="click" data-track-action="author link - scholar" data-track-label="link" rel="nofollow">Google Scholar</a></span></p></div></div></li><li id="auth-William-Hang-Aff3"><span class="c-article-authors-search__title u-h3 js-search-name">William Hang</span><div class="c-article-authors-search__list"><div class="c-article-authors-search__item c-article-authors-search__list-item--left"><a href="/search?author=William%20Hang" class="c-article-button" data-track="click" data-track-action="author link - publication" data-track-label="link" rel="nofollow">View author publications</a></div><div class="c-article-authors-search__item c-article-authors-search__list-item--right"><p class="search-in-title-js c-article-authors-search__text">You can also search for this author in <span class="c-article-identifiers"><a class="c-article-identifiers__item" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=search&term=William%20Hang" data-track="click" data-track-action="author link - pubmed" data-track-label="link" rel="nofollow">PubMed</a><span class="u-hide"> </span><a class="c-article-identifiers__item" href="http://scholar.google.co.uk/scholar?as_q=&num=10&btnG=Search+Scholar&as_epq=&as_oq=&as_eq=&as_occt=any&as_sauthors=%22William%20Hang%22&as_publication=&as_ylo=&as_yhi=&as_allsubj=all&hl=en" data-track="click" data-track-action="author link - scholar" data-track-label="link" rel="nofollow">Google Scholar</a></span></p></div></div></li><li id="auth-Emre-Tuncer-Aff2"><span class="c-article-authors-search__title u-h3 js-search-name">Emre Tuncer</span><div class="c-article-authors-search__list"><div class="c-article-authors-search__item c-article-authors-search__list-item--left"><a href="/search?author=Emre%20Tuncer" class="c-article-button" data-track="click" data-track-action="author link - publication" data-track-label="link" rel="nofollow">View author publications</a></div><div class="c-article-authors-search__item c-article-authors-search__list-item--right"><p class="search-in-title-js c-article-authors-search__text">You can also search for this author in <span class="c-article-identifiers"><a class="c-article-identifiers__item" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=search&term=Emre%20Tuncer" data-track="click" data-track-action="author link - pubmed" data-track-label="link" rel="nofollow">PubMed</a><span class="u-hide"> </span><a class="c-article-identifiers__item" href="http://scholar.google.co.uk/scholar?as_q=&num=10&btnG=Search+Scholar&as_epq=&as_oq=&as_eq=&as_occt=any&as_sauthors=%22Emre%20Tuncer%22&as_publication=&as_ylo=&as_yhi=&as_allsubj=all&hl=en" data-track="click" data-track-action="author link - scholar" data-track-label="link" rel="nofollow">Google Scholar</a></span></p></div></div></li><li id="auth-Quoc_V_-Le-Aff1"><span class="c-article-authors-search__title u-h3 js-search-name">Quoc V. Le</span><div class="c-article-authors-search__list"><div class="c-article-authors-search__item c-article-authors-search__list-item--left"><a href="/search?author=Quoc%20V.%20Le" class="c-article-button" data-track="click" data-track-action="author link - publication" data-track-label="link" rel="nofollow">View author publications</a></div><div class="c-article-authors-search__item c-article-authors-search__list-item--right"><p class="search-in-title-js c-article-authors-search__text">You can also search for this author in <span class="c-article-identifiers"><a class="c-article-identifiers__item" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=search&term=Quoc%20V.%20Le" data-track="click" data-track-action="author link - pubmed" data-track-label="link" rel="nofollow">PubMed</a><span class="u-hide"> </span><a class="c-article-identifiers__item" href="http://scholar.google.co.uk/scholar?as_q=&num=10&btnG=Search+Scholar&as_epq=&as_oq=&as_eq=&as_occt=any&as_sauthors=%22Quoc%20V.%20Le%22&as_publication=&as_ylo=&as_yhi=&as_allsubj=all&hl=en" data-track="click" data-track-action="author link - scholar" data-track-label="link" rel="nofollow">Google Scholar</a></span></p></div></div></li><li id="auth-James-Laudon-Aff1"><span class="c-article-authors-search__title u-h3 js-search-name">James Laudon</span><div class="c-article-authors-search__list"><div class="c-article-authors-search__item c-article-authors-search__list-item--left"><a href="/search?author=James%20Laudon" class="c-article-button" data-track="click" data-track-action="author link - publication" data-track-label="link" rel="nofollow">View author publications</a></div><div class="c-article-authors-search__item c-article-authors-search__list-item--right"><p class="search-in-title-js c-article-authors-search__text">You can also search for this author in <span class="c-article-identifiers"><a class="c-article-identifiers__item" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=search&term=James%20Laudon" data-track="click" data-track-action="author link - pubmed" data-track-label="link" rel="nofollow">PubMed</a><span class="u-hide"> </span><a class="c-article-identifiers__item" href="http://scholar.google.co.uk/scholar?as_q=&num=10&btnG=Search+Scholar&as_epq=&as_oq=&as_eq=&as_occt=any&as_sauthors=%22James%20Laudon%22&as_publication=&as_ylo=&as_yhi=&as_allsubj=all&hl=en" data-track="click" data-track-action="author link - scholar" data-track-label="link" rel="nofollow">Google Scholar</a></span></p></div></div></li><li id="auth-Richard-Ho-Aff2"><span class="c-article-authors-search__title u-h3 js-search-name">Richard Ho</span><div class="c-article-authors-search__list"><div class="c-article-authors-search__item c-article-authors-search__list-item--left"><a href="/search?author=Richard%20Ho" class="c-article-button" data-track="click" data-track-action="author link - publication" data-track-label="link" rel="nofollow">View author publications</a></div><div class="c-article-authors-search__item c-article-authors-search__list-item--right"><p class="search-in-title-js c-article-authors-search__text">You can also search for this author in <span class="c-article-identifiers"><a class="c-article-identifiers__item" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=search&term=Richard%20Ho" data-track="click" data-track-action="author link - pubmed" data-track-label="link" rel="nofollow">PubMed</a><span class="u-hide"> </span><a class="c-article-identifiers__item" href="http://scholar.google.co.uk/scholar?as_q=&num=10&btnG=Search+Scholar&as_epq=&as_oq=&as_eq=&as_occt=any&as_sauthors=%22Richard%20Ho%22&as_publication=&as_ylo=&as_yhi=&as_allsubj=all&hl=en" data-track="click" data-track-action="author link - scholar" data-track-label="link" rel="nofollow">Google Scholar</a></span></p></div></div></li><li id="auth-Roger-Carpenter-Aff2"><span class="c-article-authors-search__title u-h3 js-search-name">Roger Carpenter</span><div class="c-article-authors-search__list"><div class="c-article-authors-search__item c-article-authors-search__list-item--left"><a href="/search?author=Roger%20Carpenter" class="c-article-button" data-track="click" data-track-action="author link - publication" data-track-label="link" rel="nofollow">View author publications</a></div><div class="c-article-authors-search__item c-article-authors-search__list-item--right"><p class="search-in-title-js c-article-authors-search__text">You can also search for this author in <span class="c-article-identifiers"><a class="c-article-identifiers__item" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=search&term=Roger%20Carpenter" data-track="click" data-track-action="author link - pubmed" data-track-label="link" rel="nofollow">PubMed</a><span class="u-hide"> </span><a class="c-article-identifiers__item" href="http://scholar.google.co.uk/scholar?as_q=&num=10&btnG=Search+Scholar&as_epq=&as_oq=&as_eq=&as_occt=any&as_sauthors=%22Roger%20Carpenter%22&as_publication=&as_ylo=&as_yhi=&as_allsubj=all&hl=en" data-track="click" data-track-action="author link - scholar" data-track-label="link" rel="nofollow">Google Scholar</a></span></p></div></div></li><li id="auth-Jeff-Dean-Aff1"><span class="c-article-authors-search__title u-h3 js-search-name">Jeff Dean</span><div class="c-article-authors-search__list"><div class="c-article-authors-search__item c-article-authors-search__list-item--left"><a href="/search?author=Jeff%20Dean" class="c-article-button" data-track="click" data-track-action="author link - publication" data-track-label="link" rel="nofollow">View author publications</a></div><div class="c-article-authors-search__item c-article-authors-search__list-item--right"><p class="search-in-title-js c-article-authors-search__text">You can also search for this author in <span class="c-article-identifiers"><a class="c-article-identifiers__item" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=search&term=Jeff%20Dean" data-track="click" data-track-action="author link - pubmed" data-track-label="link" rel="nofollow">PubMed</a><span class="u-hide"> </span><a class="c-article-identifiers__item" href="http://scholar.google.co.uk/scholar?as_q=&num=10&btnG=Search+Scholar&as_epq=&as_oq=&as_eq=&as_occt=any&as_sauthors=%22Jeff%20Dean%22&as_publication=&as_ylo=&as_yhi=&as_allsubj=all&hl=en" data-track="click" data-track-action="author link - scholar" data-track-label="link" rel="nofollow">Google Scholar</a></span></p></div></div></li></ol></div><h3 class="c-article__sub-heading" id="contributions">Contributions</h3><p>A.G. and A.M. are co-first authors and wrote the text with senior author J.D. E.S., J.W.J., and Y.-J.L. were major contributors and ran experiments. R.C. and Y.-J.L. provided key insights and expertise in physical design throughout the drafting of this addendum. The following authors carefully reviewed the addendum and provided helpful feedback: J.P., J.L., W.H., E.T., R.H., K.S., M.Y., E.J., O.P., A.N., A.T., S.W. and Q.V.L.</p><h3 class="c-article__sub-heading" id="corresponding-author">Corresponding authors</h3><p id="corresponding-author-list">Correspondence to <a id="corresp-c1" href="mailto:agoldie@google.com">Anna Goldie</a> or <a id="corresp-c2" href="mailto:azalia@google.com">Azalia Mirhoseini</a>.</p></div></div></section><section data-title="Rights and permissions"><div class="c-article-section" id="rightslink-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="rightslink">Rights and permissions</h2><div class="c-article-section__content" id="rightslink-content"><p class="c-article-rights"><a data-track="click" data-track-action="view rights and permissions" data-track-label="link" href="https://s100.copyright.com/AppDispatchServlet?title=Addendum%3A%20A%20graph%20placement%20methodology%20for%20fast%20chip%20design&author=Anna%20Goldie%20et%20al&contentID=10.1038%2Fs41586-024-08032-5&copyright=The%20Author%28s%29%2C%20under%20exclusive%20licence%20to%20Springer%20Nature%20Limited&publication=0028-0836&publicationDate=2024-09-26&publisherName=SpringerNature&orderBeanReset=true">Reprints and permissions</a></p></div></div></section><section aria-labelledby="article-info" data-title="About this article"><div class="c-article-section" id="article-info-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="article-info">About this article</h2><div class="c-article-section__content" id="article-info-content"><div class="c-bibliographic-information"><div class="u-hide-print c-bibliographic-information__column c-bibliographic-information__column--border"><a data-crossmark="10.1038/s41586-024-08032-5" target="_blank" rel="noopener" href="https://crossmark.crossref.org/dialog/?doi=10.1038/s41586-024-08032-5" data-track="click" data-track-action="Click Crossmark" data-track-label="link" data-test="crossmark"><img loading="lazy" width="57" height="81" alt="Check for updates. Verify currency and authenticity via CrossMark" src="data:image/svg+xml;base64,<svg height="81" width="57" xmlns="http://www.w3.org/2000/svg"><g fill="none" fill-rule="evenodd"><path d="m17.35 35.45 21.3-14.2v-17.03h-21.3" fill="#989898"/><path d="m38.65 35.45-21.3-14.2v-17.03h21.3" fill="#747474"/><path d="m28 .5c-12.98 0-23.5 10.52-23.5 23.5s10.52 23.5 23.5 23.5 23.5-10.52 23.5-23.5c0-6.23-2.48-12.21-6.88-16.62-4.41-4.4-10.39-6.88-16.62-6.88zm0 41.25c-9.8 0-17.75-7.95-17.75-17.75s7.95-17.75 17.75-17.75 17.75 7.95 17.75 17.75c0 4.71-1.87 9.22-5.2 12.55s-7.84 5.2-12.55 5.2z" fill="#535353"/><path d="m41 36c-5.81 6.23-15.23 7.45-22.43 2.9-7.21-4.55-10.16-13.57-7.03-21.5l-4.92-3.11c-4.95 10.7-1.19 23.42 8.78 29.71 9.97 6.3 23.07 4.22 30.6-4.86z" fill="#9c9c9c"/><path d="m.2 58.45c0-.75.11-1.42.33-2.01s.52-1.09.91-1.5c.38-.41.83-.73 1.34-.94.51-.22 1.06-.32 1.65-.32.56 0 1.06.11 1.51.35.44.23.81.5 1.1.81l-.91 1.01c-.24-.24-.49-.42-.75-.56-.27-.13-.58-.2-.93-.2-.39 0-.73.08-1.05.23-.31.16-.58.37-.81.66-.23.28-.41.63-.53 1.04-.13.41-.19.88-.19 1.39 0 1.04.23 1.86.68 2.46.45.59 1.06.88 1.84.88.41 0 .77-.07 1.07-.23s.59-.39.85-.68l.91 1c-.38.43-.8.76-1.28.99-.47.22-1 .34-1.58.34-.59 0-1.13-.1-1.64-.31-.5-.2-.94-.51-1.31-.91-.38-.4-.67-.9-.88-1.48-.22-.59-.33-1.26-.33-2.02zm8.4-5.33h1.61v2.54l-.05 1.33c.29-.27.61-.51.96-.72s.76-.31 1.24-.31c.73 0 1.27.23 1.61.71.33.47.5 1.14.5 2.02v4.31h-1.61v-4.1c0-.57-.08-.97-.25-1.21-.17-.23-.45-.35-.83-.35-.3 0-.56.08-.79.22-.23.15-.49.36-.78.64v4.8h-1.61zm7.37 6.45c0-.56.09-1.06.26-1.51.18-.45.42-.83.71-1.14.29-.3.63-.54 1.01-.71.39-.17.78-.25 1.18-.25.47 0 .88.08 1.23.24.36.16.65.38.89.67s.42.63.54 1.03c.12.41.18.84.18 1.32 0 .32-.02.57-.07.76h-4.36c.07.62.29 1.1.65 1.44.36.33.82.5 1.38.5.29 0 .57-.04.83-.13s.51-.21.76-.37l.55 1.01c-.33.21-.69.39-1.09.53-.41.14-.83.21-1.26.21-.48 0-.92-.08-1.34-.25-.41-.16-.76-.4-1.07-.7-.31-.31-.55-.69-.72-1.13-.18-.44-.26-.95-.26-1.52zm4.6-.62c0-.55-.11-.98-.34-1.28-.23-.31-.58-.47-1.06-.47-.41 0-.77.15-1.07.45-.31.29-.5.73-.58 1.3zm2.5.62c0-.57.09-1.08.28-1.53.18-.44.43-.82.75-1.13s.69-.54 1.1-.71c.42-.16.85-.24 1.31-.24.45 0 .84.08 1.17.23s.61.34.85.57l-.77 1.02c-.19-.16-.38-.28-.56-.37-.19-.09-.39-.14-.61-.14-.56 0-1.01.21-1.35.63-.35.41-.52.97-.52 1.67 0 .69.17 1.24.51 1.66.34.41.78.62 1.32.62.28 0 .54-.06.78-.17.24-.12.45-.26.64-.42l.67 1.03c-.33.29-.69.51-1.08.65-.39.15-.78.23-1.18.23-.46 0-.9-.08-1.31-.24-.4-.16-.75-.39-1.05-.7s-.53-.69-.7-1.13c-.17-.45-.25-.96-.25-1.53zm6.91-6.45h1.58v6.17h.05l2.54-3.16h1.77l-2.35 2.8 2.59 4.07h-1.75l-1.77-2.98-1.08 1.23v1.75h-1.58zm13.69 1.27c-.25-.11-.5-.17-.75-.17-.58 0-.87.39-.87 1.16v.75h1.34v1.27h-1.34v5.6h-1.61v-5.6h-.92v-1.2l.92-.07v-.72c0-.35.04-.68.13-.98.08-.31.21-.57.4-.79s.42-.39.71-.51c.28-.12.63-.18 1.04-.18.24 0 .48.02.69.07.22.05.41.1.57.17zm.48 5.18c0-.57.09-1.08.27-1.53.17-.44.41-.82.72-1.13.3-.31.65-.54 1.04-.71.39-.16.8-.24 1.23-.24s.84.08 1.24.24c.4.17.74.4 1.04.71s.54.69.72 1.13c.19.45.28.96.28 1.53s-.09 1.08-.28 1.53c-.18.44-.42.82-.72 1.13s-.64.54-1.04.7-.81.24-1.24.24-.84-.08-1.23-.24-.74-.39-1.04-.7c-.31-.31-.55-.69-.72-1.13-.18-.45-.27-.96-.27-1.53zm1.65 0c0 .69.14 1.24.43 1.66.28.41.68.62 1.18.62.51 0 .9-.21 1.19-.62.29-.42.44-.97.44-1.66 0-.7-.15-1.26-.44-1.67-.29-.42-.68-.63-1.19-.63-.5 0-.9.21-1.18.63-.29.41-.43.97-.43 1.67zm6.48-3.44h1.33l.12 1.21h.05c.24-.44.54-.79.88-1.02.35-.24.7-.36 1.07-.36.32 0 .59.05.78.14l-.28 1.4-.33-.09c-.11-.01-.23-.02-.38-.02-.27 0-.56.1-.86.31s-.55.58-.77 1.1v4.2h-1.61zm-47.87 15h1.61v4.1c0 .57.08.97.25 1.2.17.24.44.35.81.35.3 0 .57-.07.8-.22.22-.15.47-.39.73-.73v-4.7h1.61v6.87h-1.32l-.12-1.01h-.04c-.3.36-.63.64-.98.86-.35.21-.76.32-1.24.32-.73 0-1.27-.24-1.61-.71-.33-.47-.5-1.14-.5-2.02zm9.46 7.43v2.16h-1.61v-9.59h1.33l.12.72h.05c.29-.24.61-.45.97-.63.35-.17.72-.26 1.1-.26.43 0 .81.08 1.15.24.33.17.61.4.84.71.24.31.41.68.53 1.11.13.42.19.91.19 1.44 0 .59-.09 1.11-.25 1.57-.16.47-.38.85-.65 1.16-.27.32-.58.56-.94.73-.35.16-.72.25-1.1.25-.3 0-.6-.07-.9-.2s-.59-.31-.87-.56zm0-2.3c.26.22.5.37.73.45.24.09.46.13.66.13.46 0 .84-.2 1.15-.6.31-.39.46-.98.46-1.77 0-.69-.12-1.22-.35-1.61-.23-.38-.61-.57-1.13-.57-.49 0-.99.26-1.52.77zm5.87-1.69c0-.56.08-1.06.25-1.51.16-.45.37-.83.65-1.14.27-.3.58-.54.93-.71s.71-.25 1.08-.25c.39 0 .73.07 1 .2.27.14.54.32.81.55l-.06-1.1v-2.49h1.61v9.88h-1.33l-.11-.74h-.06c-.25.25-.54.46-.88.64-.33.18-.69.27-1.06.27-.87 0-1.56-.32-2.07-.95s-.76-1.51-.76-2.65zm1.67-.01c0 .74.13 1.31.4 1.7.26.38.65.58 1.15.58.51 0 .99-.26 1.44-.77v-3.21c-.24-.21-.48-.36-.7-.45-.23-.08-.46-.12-.7-.12-.45 0-.82.19-1.13.59-.31.39-.46.95-.46 1.68zm6.35 1.59c0-.73.32-1.3.97-1.71.64-.4 1.67-.68 3.08-.84 0-.17-.02-.34-.07-.51-.05-.16-.12-.3-.22-.43s-.22-.22-.38-.3c-.15-.06-.34-.1-.58-.1-.34 0-.68.07-1 .2s-.63.29-.93.47l-.59-1.08c.39-.24.81-.45 1.28-.63.47-.17.99-.26 1.54-.26.86 0 1.51.25 1.93.76s.63 1.25.63 2.21v4.07h-1.32l-.12-.76h-.05c-.3.27-.63.48-.98.66s-.73.27-1.14.27c-.61 0-1.1-.19-1.48-.56-.38-.36-.57-.85-.57-1.46zm1.57-.12c0 .3.09.53.27.67.19.14.42.21.71.21.28 0 .54-.07.77-.2s.48-.31.73-.56v-1.54c-.47.06-.86.13-1.18.23-.31.09-.57.19-.76.31s-.33.25-.41.4c-.09.15-.13.31-.13.48zm6.29-3.63h-.98v-1.2l1.06-.07.2-1.88h1.34v1.88h1.75v1.27h-1.75v3.28c0 .8.32 1.2.97 1.2.12 0 .24-.01.37-.04.12-.03.24-.07.34-.11l.28 1.19c-.19.06-.4.12-.64.17-.23.05-.49.08-.76.08-.4 0-.74-.06-1.02-.18-.27-.13-.49-.3-.67-.52-.17-.21-.3-.48-.37-.78-.08-.3-.12-.64-.12-1.01zm4.36 2.17c0-.56.09-1.06.27-1.51s.41-.83.71-1.14c.29-.3.63-.54 1.01-.71.39-.17.78-.25 1.18-.25.47 0 .88.08 1.23.24.36.16.65.38.89.67s.42.63.54 1.03c.12.41.18.84.18 1.32 0 .32-.02.57-.07.76h-4.37c.08.62.29 1.1.65 1.44.36.33.82.5 1.38.5.3 0 .58-.04.84-.13.25-.09.51-.21.76-.37l.54 1.01c-.32.21-.69.39-1.09.53s-.82.21-1.26.21c-.47 0-.92-.08-1.33-.25-.41-.16-.77-.4-1.08-.7-.3-.31-.54-.69-.72-1.13-.17-.44-.26-.95-.26-1.52zm4.61-.62c0-.55-.11-.98-.34-1.28-.23-.31-.58-.47-1.06-.47-.41 0-.77.15-1.08.45-.31.29-.5.73-.57 1.3zm3.01 2.23c.31.24.61.43.92.57.3.13.63.2.98.2.38 0 .65-.08.83-.23s.27-.35.27-.6c0-.14-.05-.26-.13-.37-.08-.1-.2-.2-.34-.28-.14-.09-.29-.16-.47-.23l-.53-.22c-.23-.09-.46-.18-.69-.3-.23-.11-.44-.24-.62-.4s-.33-.35-.45-.55c-.12-.21-.18-.46-.18-.75 0-.61.23-1.1.68-1.49.44-.38 1.06-.57 1.83-.57.48 0 .91.08 1.29.25s.71.36.99.57l-.74.98c-.24-.17-.49-.32-.73-.42-.25-.11-.51-.16-.78-.16-.35 0-.6.07-.76.21-.17.15-.25.33-.25.54 0 .14.04.26.12.36s.18.18.31.26c.14.07.29.14.46.21l.54.19c.23.09.47.18.7.29s.44.24.64.4c.19.16.34.35.46.58.11.23.17.5.17.82 0 .3-.06.58-.17.83-.12.26-.29.48-.51.68-.23.19-.51.34-.84.45-.34.11-.72.17-1.15.17-.48 0-.95-.09-1.41-.27-.46-.19-.86-.41-1.2-.68z" fill="#535353"/></g></svg>"></a></div><div class="c-bibliographic-information__column"><h3 class="c-article__sub-heading" id="citeas">Cite this article</h3><p class="c-bibliographic-information__citation">Goldie, A., Mirhoseini, A., Yazgan, M. <i>et al.</i> Addendum: A graph placement methodology for fast chip design. <i>Nature</i> <b>634</b>, E10–E11 (2024). https://doi.org/10.1038/s41586-024-08032-5</p><p class="c-bibliographic-information__download-citation u-hide-print"><a data-test="citation-link" data-track="click" data-track-action="download article citation" data-track-label="link" data-track-external="" rel="nofollow" href="https://citation-needed.springer.com/v2/references/10.1038/s41586-024-08032-5?format=refman&flavour=citation">Download citation<svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-download-medium"></use></svg></a></p><ul class="c-bibliographic-information__list" data-test="publication-history"><li class="c-bibliographic-information__list-item"><p>Published<span class="u-hide">: </span><span class="c-bibliographic-information__value"><time datetime="2024-09-26">26 September 2024</time></span></p></li><li class="c-bibliographic-information__list-item"><p>Issue Date<span class="u-hide">: </span><span class="c-bibliographic-information__value"><time datetime="2024-10-17">17 October 2024</time></span></p></li><li class="c-bibliographic-information__list-item c-bibliographic-information__list-item--full-width"><p><abbr title="Digital Object Identifier">DOI</abbr><span class="u-hide">: </span><span class="c-bibliographic-information__value">https://doi.org/10.1038/s41586-024-08032-5</span></p></li></ul><div data-component="share-box"><div class="c-article-share-box u-display-none" hidden=""><h3 class="c-article__sub-heading">Share this article</h3><p class="c-article-share-box__description">Anyone you share the following link with will be able to read this content:</p><button class="js-get-share-url c-article-share-box__button" type="button" id="get-share-url" data-track="click" data-track-label="button" data-track-external="" data-track-action="get shareable link">Get shareable link</button><div class="js-no-share-url-container u-display-none" hidden=""><p class="js-c-article-share-box__no-sharelink-info c-article-share-box__no-sharelink-info">Sorry, a shareable link is not currently available for this article.</p></div><div class="js-share-url-container u-display-none" hidden=""><p class="js-share-url c-article-share-box__only-read-input" id="share-url" data-track="click" data-track-label="button" data-track-action="select share url"></p><button class="js-copy-share-url c-article-share-box__button--link-like" type="button" id="copy-share-url" data-track="click" data-track-label="button" data-track-action="copy share url" data-track-external="">Copy to clipboard</button></div><p class="js-c-article-share-box__additional-info c-article-share-box__additional-info"> Provided by the Springer Nature SharedIt content-sharing initiative </p></div></div><div data-component="article-info-list"></div></div></div></div></div></section> </div> </div> </article> </main> <aside class="c-article-extras u-hide-print" aria-label="Article navigation" data-component-reading-companion data-container-type="reading-companion" data-track-component="reading companion"> <div class="js-context-bar-sticky-point-desktop" data-track-context="reading companion"> <noscript> <div class="c-nature-box c-nature-box--side " data-component="entitlement-box"> <p class="c-nature-box__text js-text">You have full access to this article via your institution.</p> <div class="c-pdf-download u-clear-both js-pdf-download"> <a href="/articles/s41586-024-08032-5.pdf" class="u-button u-button--full-width u-button--primary u-justify-content-space-between c-pdf-download__link" data-article-pdf="true" data-readcube-pdf-url="true" data-test="download-pdf" data-draft-ignore="true" data-track="content_download" data-track-type="article pdf download" data-track-action="download pdf" data-track-label="link" data-track-external download> <span class="c-pdf-download__text">Download PDF</span> <svg aria-hidden="true" focusable="false" width="16" height="16" class="u-icon"><use xlink:href="#icon-download"/></svg> </a> </div> </div> </noscript> <div class="c-nature-box__wrapper c-nature-box__wrapper--placeholder"> <div class="c-nature-box c-nature-box--side u-display-none u-hide-print" aria-hidden="true" data-component="entitlement-box" id=entitlement-box-right-column > <p class="c-nature-box__text js-text u-display-none" aria-hidden="true"></p> <div class="c-pdf-download u-clear-both js-pdf-download"> <a href="/articles/s41586-024-08032-5.pdf" class="u-button u-button--full-width u-button--primary u-justify-content-space-between c-pdf-download__link" data-article-pdf="true" data-readcube-pdf-url="true" data-test="download-pdf" data-draft-ignore="true" data-track="content_download" data-track-type="article pdf download" data-track-action="download pdf" data-track-label="link" data-track-external download> <span class="c-pdf-download__text">Download PDF</span> <svg aria-hidden="true" focusable="false" width="16" height="16" class="u-icon"><use xlink:href="#icon-download"/></svg> </a> </div> </div> </div> </div> <div class="c-reading-companion"> <div class="c-reading-companion__sticky" data-component="reading-companion-sticky" data-test="reading-companion-sticky"> <div class="c-reading-companion__panel c-reading-companion__sections c-reading-companion__panel--active" id="tabpanel-sections"> <div class="u-lazy-ad-wrapper u-mt-16 u-hide" data-component-mpu> <div class="c-ad c-ad--300x250"> <div class="c-ad__inner"> <p class="c-ad__label">Advertisement</p> <div id="div-gpt-ad-right-2" class="div-gpt-ad advert medium-rectangle js-ad text-center hide-print grade-c-hide" data-ad-type="right" data-test="right-ad" data-pa11y-ignore data-gpt data-gpt-unitpath="/285/nature.com/article" data-gpt-sizes="300x250" data-gpt-targeting="type=article;pos=right;artid=s41586-024-08032-5;doi=10.1038/s41586-024-08032-5;techmeta=119;subjmeta=1042,166,639,705,987;kwrd=Computational+science,Electrical+and+electronic+engineering"> <noscript> <a href="//pubads.g.doubleclick.net/gampad/jump?iu=/285/nature.com/article&sz=300x250&c=1189392030&t=pos%3Dright%26type%3Darticle%26artid%3Ds41586-024-08032-5%26doi%3D10.1038/s41586-024-08032-5%26techmeta%3D119%26subjmeta%3D1042,166,639,705,987%26kwrd%3DComputational+science,Electrical+and+electronic+engineering"> <img data-test="gpt-advert-fallback-img" src="//pubads.g.doubleclick.net/gampad/ad?iu=/285/nature.com/article&sz=300x250&c=1189392030&t=pos%3Dright%26type%3Darticle%26artid%3Ds41586-024-08032-5%26doi%3D10.1038/s41586-024-08032-5%26techmeta%3D119%26subjmeta%3D1042,166,639,705,987%26kwrd%3DComputational+science,Electrical+and+electronic+engineering" alt="Advertisement" width="300" height="250"></a> </noscript> </div> </div> </div> </div> </div> <div class="c-reading-companion__panel c-reading-companion__figures c-reading-companion__panel--full-width" id="tabpanel-figures"></div> <div class="c-reading-companion__panel c-reading-companion__references c-reading-companion__panel--full-width" id="tabpanel-references"></div> </div> </div> </aside> </div> <nav class="c-header__dropdown" aria-labelledby="Explore-content" data-test="Explore-content" id="explore" data-track-component="nature-150-split-header"> <div class="c-header__container"> <h2 id="Explore-content" class="c-header__heading c-header__heading--js-hide">Explore content</h2> <ul class="c-header__list c-header__list--js-stack"> <li class="c-header__item"> <a class="c-header__link" href="/nature/research-articles" data-track="click" data-track-action="research articles" data-track-label="link" data-test="explore-nav-item"> Research articles </a> </li> <li class="c-header__item"> <a class="c-header__link" href="/news" data-track="click" data-track-action="news" data-track-label="link" data-test="explore-nav-item"> News </a> </li> <li class="c-header__item"> <a class="c-header__link" href="/opinion" data-track="click" data-track-action="opinion" data-track-label="link" data-test="explore-nav-item"> Opinion </a> </li> <li class="c-header__item"> <a class="c-header__link" href="/research-analysis" data-track="click" data-track-action="research analysis" data-track-label="link" data-test="explore-nav-item"> Research Analysis </a> </li> <li class="c-header__item"> <a class="c-header__link" href="/careers" data-track="click" data-track-action="careers" data-track-label="link" data-test="explore-nav-item"> Careers </a> </li> <li class="c-header__item"> <a class="c-header__link" href="/books-culture" data-track="click" data-track-action="books & culture" data-track-label="link" data-test="explore-nav-item"> Books & Culture </a> </li> <li class="c-header__item"> <a class="c-header__link" href="/nature/podcasts" data-track="click" data-track-action="podcasts" data-track-label="link" data-test="explore-nav-item"> Podcasts </a> </li> <li class="c-header__item"> <a class="c-header__link" href="/nature/videos" data-track="click" data-track-action="videos" data-track-label="link" data-test="explore-nav-item"> Videos </a> </li> <li class="c-header__item"> <a class="c-header__link" href="/nature/current-issue" data-track="click" data-track-action="current issue" data-track-label="link" data-test="explore-nav-item"> Current issue </a> </li> <li class="c-header__item"> <a class="c-header__link" href="/nature/browse-issues" data-track="click" data-track-action="browse issues" data-track-label="link" data-test="explore-nav-item"> Browse issues </a> </li> <li class="c-header__item"> <a class="c-header__link" href="/nature/collections" data-track="click" data-track-action="collections" data-track-label="link" data-test="explore-nav-item"> Collections </a> </li> <li class="c-header__item"> <a class="c-header__link" href="/nature/browse-subjects" data-track="click" data-track-action="subjects" data-track-label="link" data-test="explore-nav-item"> Subjects </a> </li> </ul> <ul class="c-header__list c-header__list--js-stack"> <li class="c-header__item"> <a class="c-header__link" href="https://www.facebook.com/Nature" data-track="click" data-track-action="facebook" data-track-label="link">Follow us on Facebook </a> </li> <li class="c-header__item"> <a class="c-header__link" href="https://twitter.com/nature" data-track="click" data-track-action="twitter" data-track-label="link">Follow us on Twitter </a> </li> <li class="c-header__item c-header__item--hide-lg"> <a class="c-header__link" href="https://www.nature.com/my-account/alerts/subscribe-journal?list-id=1" rel="nofollow" data-track="click" data-track-action="Sign up for alerts" data-track-external data-track-label="link (mobile dropdown)">Sign up for alerts<svg role="img" aria-hidden="true" focusable="false" height="18" viewBox="0 0 18 18" width="18" xmlns="http://www.w3.org/2000/svg"><path d="m4 10h2.5c.27614237 0 .5.2238576.5.5s-.22385763.5-.5.5h-3.08578644l-1.12132034 1.1213203c-.18753638.1875364-.29289322.4418903-.29289322.7071068v.1715729h14v-.1715729c0-.2652165-.1053568-.5195704-.2928932-.7071068l-1.7071068-1.7071067v-3.4142136c0-2.76142375-2.2385763-5-5-5-2.76142375 0-5 2.23857625-5 5zm3 4c0 1.1045695.8954305 2 2 2s2-.8954305 2-2zm-5 0c-.55228475 0-1-.4477153-1-1v-.1715729c0-.530433.21071368-1.0391408.58578644-1.4142135l1.41421356-1.4142136v-3c0-3.3137085 2.6862915-6 6-6s6 2.6862915 6 6v3l1.4142136 1.4142136c.3750727.3750727.5857864.8837805.5857864 1.4142135v.1715729c0 .5522847-.4477153 1-1 1h-4c0 1.6568542-1.3431458 3-3 3-1.65685425 0-3-1.3431458-3-3z" fill="#fff"/></svg> </a> </li> <li class="c-header__item c-header__item--hide-lg"> <a class="c-header__link" href="https://www.nature.com/nature.rss" data-track="click" data-track-action="rss feed" data-track-label="link"> <span>RSS feed</span> </a> </li> </ul> </div> </nav> <nav class="c-header__dropdown" aria-labelledby="About-the-journal" id="about-the-journal" data-test="about-the-journal" data-track-component="nature-150-split-header"> <div class="c-header__container"> <h2 id="About-the-journal" class="c-header__heading c-header__heading--js-hide">About the journal</h2> <ul class="c-header__list c-header__list--js-stack"> <li class="c-header__item"> <a class="c-header__link" href="/nature/journal-staff" data-track="click" data-track-action="journal staff" data-track-label="link"> Journal Staff </a> </li> <li class="c-header__item"> <a class="c-header__link" href="/nature/editors" data-track="click" data-track-action="about the editors" data-track-label="link"> About the Editors </a> </li> <li class="c-header__item"> <a class="c-header__link" href="/nature/journal-information" data-track="click" data-track-action="journal information" data-track-label="link"> Journal Information </a> </li> <li class="c-header__item"> <a class="c-header__link" href="/nature/our-publishing-models" data-track="click" data-track-action="our publishing models" data-track-label="link"> Our publishing models </a> </li> <li class="c-header__item"> <a class="c-header__link" href="/nature/editorial-values-statement" data-track="click" data-track-action="editorial values statement" data-track-label="link"> Editorial Values Statement </a> </li> <li class="c-header__item"> <a class="c-header__link" href="/nature/journal-impact" data-track="click" data-track-action="journal metrics" data-track-label="link"> Journal Metrics </a> </li> <li class="c-header__item"> <a class="c-header__link" href="/nature/awards" data-track="click" data-track-action="awards" data-track-label="link"> Awards </a> </li> <li class="c-header__item"> <a class="c-header__link" href="/nature/contact" data-track="click" data-track-action="contact" data-track-label="link"> Contact </a> </li> <li class="c-header__item"> <a class="c-header__link" href="/nature/editorial-policies" data-track="click" data-track-action="editorial policies" data-track-label="link"> Editorial policies </a> </li> <li class="c-header__item"> <a class="c-header__link" href="/nature/history-of-nature" data-track="click" data-track-action="history of nature" data-track-label="link"> History of Nature </a> </li> <li class="c-header__item"> <a class="c-header__link" href="/nature/send-a-news-tip" data-track="click" data-track-action="send a news tip" data-track-label="link"> Send a news tip </a> </li> </ul> </div> </nav> <nav class="c-header__dropdown" aria-labelledby="Publish-with-us-label" id="publish-with-us" data-test="publish-with-us" data-track-component="nature-150-split-header"> <div class="c-header__container"> <h2 id="Publish-with-us-label" class="c-header__heading c-header__heading--js-hide">Publish with us</h2> <ul class="c-header__list c-header__list--js-stack"> <li class="c-header__item"> <a class="c-header__link" href="/nature/for-authors" data-track="click" data-track-action="for authors" data-track-label="link"> For Authors </a> </li> <li class="c-header__item"> <a class="c-header__link" href="/nature/for-referees" data-track="click" data-track-action="for referees" data-track-label="link"> For Referees </a> </li> <li class="c-header__item"> <a class="c-header__link" data-test="nature-author-services" data-track="nav_language_services" data-track-context="header publish with us dropdown menu" data-track-action="manuscript author services" data-track-label="link manuscript author services" href="https://authorservices.springernature.com/go/sn/?utm_source=For+Authors&utm_medium=Website_Nature&utm_campaign=Platform+Experimentation+2022&utm_id=PE2022"> Language editing services </a> </li> <li class="c-header__item c-header__item--keyline"> <a class="c-header__link" href="https://mts-nature.nature.com/" data-track="click_submit_manuscript" data-track-context="submit link in Nature header dropdown menu" data-track-action="submit manuscript" data-track-label="link (publish with us dropdown menu)" data-track-external>Submit manuscript<svg role="img" aria-hidden="true" focusable="false" height="18" viewBox="0 0 18 18" width="18" xmlns="http://www.w3.org/2000/svg"><path d="m15 0c1.1045695 0 2 .8954305 2 2v5.5c0 .27614237-.2238576.5-.5.5s-.5-.22385763-.5-.5v-5.5c0-.51283584-.3860402-.93550716-.8833789-.99327227l-.1166211-.00672773h-9v3c0 1.1045695-.8954305 2-2 2h-3v10c0 .5128358.38604019.9355072.88337887.9932723l.11662113.0067277h7.5c.27614237 0 .5.2238576.5.5s-.22385763.5-.5.5h-7.5c-1.1045695 0-2-.8954305-2-2v-10.17157288c0-.53043297.21071368-1.0391408.58578644-1.41421356l3.82842712-3.82842712c.37507276-.37507276.88378059-.58578644 1.41421356-.58578644zm-.5442863 8.18867991 3.3545404 3.35454039c.2508994.2508994.2538696.6596433.0035959.909917-.2429543.2429542-.6561449.2462671-.9065387-.0089489l-2.2609825-2.3045251.0010427 7.2231989c0 .3569916-.2898381.6371378-.6473715.6371378-.3470771 0-.6473715-.2852563-.6473715-.6371378l-.0010428-7.2231995-2.2611222 2.3046654c-.2531661.2580415-.6562868.2592444-.9065605.0089707-.24295423-.2429542-.24865597-.6576651.0036132-.9099343l3.3546673-3.35466731c.2509089-.25090888.6612706-.25227691.9135302-.00001728zm-.9557137-3.18867991c.2761424 0 .5.22385763.5.5s-.2238576.5-.5.5h-6c-.27614237 0-.5-.22385763-.5-.5s.22385763-.5.5-.5zm-8.5-3.587-3.587 3.587h2.587c.55228475 0 1-.44771525 1-1zm8.5 1.587c.2761424 0 .5.22385763.5.5s-.2238576.5-.5.5h-6c-.27614237 0-.5-.22385763-.5-.5s.22385763-.5.5-.5z" fill="#fff"/></svg> </a> </li> </ul> </div> </nav> <div id="search-menu" class="c-header__dropdown c-header__dropdown--full-width" data-track-component="nature-150-split-header"> <div class="c-header__container"> <h2 class="c-header__visually-hidden">Search</h2> <form class="c-header__search-form" action="/search" method="get" role="search" autocomplete="off" data-test="inline-search"> <label class="c-header__heading" for="keywords">Search articles by subject, keyword or author</label> <div class="c-header__search-layout c-header__search-layout--max-width"> <div> <input type="text" required="" class="c-header__input" id="keywords" name="q" value=""> </div> <div class="c-header__search-layout"> <div> <label for="results-from" class="c-header__visually-hidden">Show results from</label> <select id="results-from" name="journal" class="c-header__select"> <option value="" selected>All journals</option> <option value="nature">This journal</option> </select> </div> <div> <button type="submit" class="c-header__search-button">Search</button> </div> </div> </div> </form> <div class="c-header__flush"> <a class="c-header__link" href="/search/advanced" data-track="click" data-track-action="advanced search" data-track-label="link"> Advanced search </a> </div> <h3 class="c-header__heading c-header__heading--keyline">Quick links</h3> <ul class="c-header__list"> <li><a class="c-header__link" href="/subjects" data-track="click" data-track-action="explore articles by subject" data-track-label="link">Explore articles by subject</a></li> <li><a class="c-header__link" href="/naturecareers" data-track="click" data-track-action="find a job" data-track-label="link">Find a job</a></li> <li><a class="c-header__link" href="/authors/index.html" data-track="click" data-track-action="guide to authors" data-track-label="link">Guide to authors</a></li> <li><a class="c-header__link" href="/authors/editorial_policies/" data-track="click" data-track-action="editorial policies" data-track-label="link">Editorial policies</a></li> </ul> </div> </div> <footer class="composite-layer" itemscope itemtype="http://schema.org/Periodical"> <meta itemprop="publisher" content="Springer Nature"> <div class="u-mt-16 u-mb-16"> <div class="u-container"> <div class="u-display-flex u-flex-wrap u-justify-content-space-between"> <p class="c-meta u-ma-0 u-flex-shrink"> <span class="c-meta__item"> Nature (<i>Nature</i>) </span> <span class="c-meta__item"> <abbr title="International Standard Serial Number">ISSN</abbr> <span itemprop="onlineIssn">1476-4687</span> (online) </span> <span class="c-meta__item"> <abbr title="International Standard Serial Number">ISSN</abbr> <span itemprop="printIssn">0028-0836</span> (print) </span> </p> </div> </div> </div> <div class="c-footer"> <div class="u-hide-print" data-track-component="footer"> <h2 class="u-visually-hidden">nature.com sitemap</h2> <div class="c-footer__container"> <div class="c-footer__grid c-footer__group--separator"> <div class="c-footer__group"> <h3 class="c-footer__heading u-mt-0">About Nature Portfolio</h3> <ul class="c-footer__list"> <li class="c-footer__item"><a class="c-footer__link" href="https://www.nature.com/npg_/company_info/index.html" data-track="click" data-track-action="about us" data-track-label="link">About us</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://www.nature.com/npg_/press_room/press_releases.html" data-track="click" data-track-action="press releases" data-track-label="link">Press releases</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://press.nature.com/" data-track="click" data-track-action="press office" data-track-label="link">Press office</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://support.nature.com/support/home" data-track="click" data-track-action="contact us" data-track-label="link">Contact us</a></li> </ul> </div> <div class="c-footer__group"> <h3 class="c-footer__heading u-mt-0">Discover content</h3> <ul class="c-footer__list"> <li class="c-footer__item"><a class="c-footer__link" href="https://www.nature.com/siteindex" data-track="click" data-track-action="journals a-z" data-track-label="link">Journals A-Z</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://www.nature.com/subjects" data-track="click" data-track-action="article by subject" data-track-label="link">Articles by subject</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://www.protocols.io/" data-track="click" data-track-action="protocols.io" data-track-label="link">protocols.io</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://www.natureindex.com/" data-track="click" data-track-action="nature index" data-track-label="link">Nature Index</a></li> </ul> </div> <div class="c-footer__group"> <h3 class="c-footer__heading u-mt-0">Publishing policies</h3> <ul class="c-footer__list"> <li class="c-footer__item"><a class="c-footer__link" href="https://www.nature.com/authors/editorial_policies" data-track="click" data-track-action="Nature portfolio policies" data-track-label="link">Nature portfolio policies</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://www.nature.com/nature-research/open-access" data-track="click" data-track-action="open access" data-track-label="link">Open access</a></li> </ul> </div> <div class="c-footer__group"> <h3 class="c-footer__heading u-mt-0">Author & Researcher services</h3> <ul class="c-footer__list"> <li class="c-footer__item"><a class="c-footer__link" href="https://www.nature.com/reprints" data-track="click" data-track-action="reprints and permissions" data-track-label="link">Reprints & permissions</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://www.springernature.com/gp/authors/research-data" data-track="click" data-track-action="data research service" data-track-label="link">Research data</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://authorservices.springernature.com/language-editing/" data-track="click" data-track-action="language editing" data-track-label="link">Language editing</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://authorservices.springernature.com/scientific-editing/" data-track="click" data-track-action="scientific editing" data-track-label="link">Scientific editing</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://masterclasses.nature.com/" data-track="click" data-track-action="nature masterclasses" data-track-label="link">Nature Masterclasses</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://solutions.springernature.com/" data-track="click" data-track-action="research solutions" data-track-label="link">Research Solutions</a></li> </ul> </div> <div class="c-footer__group"> <h3 class="c-footer__heading u-mt-0">Libraries & institutions</h3> <ul class="c-footer__list"> <li class="c-footer__item"><a class="c-footer__link" href="https://www.springernature.com/gp/librarians/tools-services" data-track="click" data-track-action="librarian service and tools" data-track-label="link">Librarian service & tools</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://www.springernature.com/gp/librarians/manage-your-account/librarianportal" data-track="click" data-track-action="librarian portal" data-track-label="link">Librarian portal</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://www.nature.com/openresearch/about-open-access/information-for-institutions" data-track="click" data-track-action="open research" data-track-label="link">Open research</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://www.springernature.com/gp/librarians/recommend-to-your-library" data-track="click" data-track-action="Recommend to library" data-track-label="link">Recommend to library</a></li> </ul> </div> <div class="c-footer__group"> <h3 class="c-footer__heading u-mt-0">Advertising & partnerships</h3> <ul class="c-footer__list"> <li class="c-footer__item"><a class="c-footer__link" href="https://partnerships.nature.com/product/digital-advertising/" data-track="click" data-track-action="advertising" data-track-label="link">Advertising</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://partnerships.nature.com/" data-track="click" data-track-action="partnerships and services" data-track-label="link">Partnerships & Services</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://partnerships.nature.com/media-kits/" data-track="click" data-track-action="media kits" data-track-label="link">Media kits</a> </li> <li class="c-footer__item"><a class="c-footer__link" href="https://partnerships.nature.com/product/branded-content-native-advertising/" data-track-action="branded content" data-track-label="link">Branded content</a></li> </ul> </div> <div class="c-footer__group"> <h3 class="c-footer__heading u-mt-0">Professional development</h3> <ul class="c-footer__list"> <li class="c-footer__item"><a class="c-footer__link" href="https://www.nature.com/naturecareers/" data-track="click" data-track-action="nature careers" data-track-label="link">Nature Careers</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://conferences.nature.com" data-track="click" data-track-action="nature conferences" data-track-label="link">Nature<span class="u-visually-hidden"> </span> Conferences</a></li> </ul> </div> <div class="c-footer__group"> <h3 class="c-footer__heading u-mt-0">Regional websites</h3> <ul class="c-footer__list"> <li class="c-footer__item"><a class="c-footer__link" href="https://www.nature.com/natafrica" data-track="click" data-track-action="nature africa" data-track-label="link">Nature Africa</a></li> <li class="c-footer__item"><a class="c-footer__link" href="http://www.naturechina.com" data-track="click" data-track-action="nature china" data-track-label="link">Nature China</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://www.nature.com/nindia" data-track="click" data-track-action="nature india" data-track-label="link">Nature India</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://www.nature.com/natitaly" data-track="click" data-track-action="nature Italy" data-track-label="link">Nature Italy</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://www.natureasia.com/ja-jp" data-track="click" data-track-action="nature japan" data-track-label="link">Nature Japan</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://www.nature.com/nmiddleeast" data-track="click" data-track-action="nature middle east" data-track-label="link">Nature Middle East</a></li> </ul> </div> </div> </div> <div class="c-footer__container"> <ul class="c-footer__links"> <li class="c-footer__item"><a class="c-footer__link" href="https://www.nature.com/info/privacy" data-track="click" data-track-action="privacy policy" data-track-label="link">Privacy Policy</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://www.nature.com/info/cookies" data-track="click" data-track-action="use of cookies" data-track-label="link">Use of cookies</a></li> <li class="c-footer__item"> <button class="optanon-toggle-display c-footer__link" onclick="javascript:;" data-cc-action="preferences" data-track="click" data-track-action="manage cookies" data-track-label="link">Your privacy choices/Manage cookies </button> </li> <li class="c-footer__item"><a class="c-footer__link" href="https://www.nature.com/info/legal-notice" data-track="click" data-track-action="legal notice" data-track-label="link">Legal notice</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://www.nature.com/info/accessibility-statement" data-track="click" data-track-action="accessibility statement" data-track-label="link">Accessibility statement</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://www.nature.com/info/terms-and-conditions" data-track="click" data-track-action="terms and conditions" data-track-label="link">Terms & Conditions</a></li> <li class="c-footer__item"><a class="c-footer__link" href="https://www.springernature.com/ccpa" data-track="click" data-track-action="california privacy statement" data-track-label="link">Your US state privacy rights</a></li> </ul> </div> </div> <div class="c-footer__container"> <a href="https://www.springernature.com/" class="c-footer__link"> <img src="/static/images/logos/sn-logo-white-ea63208b81.svg" alt="Springer Nature" loading="lazy" width="200" height="20"/> </a> <p class="c-footer__legal" data-test="copyright">© 2024 Springer Nature Limited</p> </div> </div> <div class="u-visually-hidden" aria-hidden="true"> <?xml version="1.0" encoding="UTF-8"?><!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN" "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd"><svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="a" d="M0 .74h56.72v55.24H0z"/></defs><symbol id="icon-access" viewBox="0 0 18 18"><path d="m14 8c.5522847 0 1 .44771525 1 1v7h2.5c.2761424 0 .5.2238576.5.5v1.5h-18v-1.5c0-.2761424.22385763-.5.5-.5h2.5v-7c0-.55228475.44771525-1 1-1s1 .44771525 1 1v6.9996556h8v-6.9996556c0-.55228475.4477153-1 1-1zm-8 0 2 1v5l-2 1zm6 0v7l-2-1v-5zm-2.42653766-7.59857636 7.03554716 4.92488299c.4162533.29137735.5174853.86502537.226108 1.28127873-.1721584.24594054-.4534847.39241464-.7536934.39241464h-14.16284822c-.50810197 0-.92-.41189803-.92-.92 0-.30020869.1464741-.58153499.39241464-.75369337l7.03554714-4.92488299c.34432015-.2410241.80260453-.2410241 1.14692468 0zm-.57346234 2.03988748-3.65526982 2.55868888h7.31053962z" fill-rule="evenodd"/></symbol><symbol id="icon-account" viewBox="0 0 18 18"><path d="m10.2379028 16.9048051c1.3083556-.2032362 2.5118471-.7235183 3.5294683-1.4798399-.8731327-2.5141501-2.0638925-3.935978-3.7673711-4.3188248v-1.27684611c1.1651924-.41183641 2-1.52307546 2-2.82929429 0-1.65685425-1.3431458-3-3-3-1.65685425 0-3 1.34314575-3 3 0 1.30621883.83480763 2.41745788 2 2.82929429v1.27684611c-1.70347856.3828468-2.89423845 1.8046747-3.76737114 4.3188248 1.01762123.7563216 2.22111275 1.2766037 3.52946833 1.4798399.40563808.0629726.81921174.0951949 1.23790281.0951949s.83226473-.0322223 1.2379028-.0951949zm4.3421782-2.1721994c1.4927655-1.4532925 2.419919-3.484675 2.419919-5.7326057 0-4.418278-3.581722-8-8-8s-8 3.581722-8 8c0 2.2479307.92715352 4.2793132 2.41991895 5.7326057.75688473-2.0164459 1.83949951-3.6071894 3.48926591-4.3218837-1.14534283-.70360829-1.90918486-1.96796271-1.90918486-3.410722 0-2.209139 1.790861-4 4-4s4 1.790861 4 4c0 1.44275929-.763842 2.70711371-1.9091849 3.410722 1.6497664.7146943 2.7323812 2.3054378 3.4892659 4.3218837zm-5.580081 3.2673943c-4.97056275 0-9-4.0294373-9-9 0-4.97056275 4.02943725-9 9-9 4.9705627 0 9 4.02943725 9 9 0 4.9705627-4.0294373 9-9 9z" fill-rule="evenodd"/></symbol><symbol id="icon-alert" viewBox="0 0 18 18"><path d="m4 10h2.5c.27614237 0 .5.2238576.5.5s-.22385763.5-.5.5h-3.08578644l-1.12132034 1.1213203c-.18753638.1875364-.29289322.4418903-.29289322.7071068v.1715729h14v-.1715729c0-.2652165-.1053568-.5195704-.2928932-.7071068l-1.7071068-1.7071067v-3.4142136c0-2.76142375-2.2385763-5-5-5-2.76142375 0-5 2.23857625-5 5zm3 4c0 1.1045695.8954305 2 2 2s2-.8954305 2-2zm-5 0c-.55228475 0-1-.4477153-1-1v-.1715729c0-.530433.21071368-1.0391408.58578644-1.4142135l1.41421356-1.4142136v-3c0-3.3137085 2.6862915-6 6-6s6 2.6862915 6 6v3l1.4142136 1.4142136c.3750727.3750727.5857864.8837805.5857864 1.4142135v.1715729c0 .5522847-.4477153 1-1 1h-4c0 1.6568542-1.3431458 3-3 3-1.65685425 0-3-1.3431458-3-3z" fill-rule="evenodd"/></symbol><symbol id="icon-arrow-broad" viewBox="0 0 16 16"><path d="m6.10307866 2.97190702v7.69043288l2.44965196-2.44676915c.38776071-.38730439 1.0088052-.39493524 1.38498697-.01919617.38609051.38563612.38643641 1.01053024-.00013864 1.39665039l-4.12239817 4.11754683c-.38616704.3857126-1.01187344.3861062-1.39846576-.0000311l-4.12258206-4.11773056c-.38618426-.38572979-.39254614-1.00476697-.01636437-1.38050605.38609047-.38563611 1.01018509-.38751562 1.4012233.00306241l2.44985644 2.4469734v-8.67638639c0-.54139983.43698413-.98042709.98493125-.98159081l7.89910522-.0043627c.5451687 0 .9871152.44142642.9871152.98595351s-.4419465.98595351-.9871152.98595351z" fill-rule="evenodd" transform="matrix(-1 0 0 -1 14 15)"/></symbol><symbol id="icon-arrow-down" viewBox="0 0 16 16"><path d="m3.28337502 11.5302405 4.03074001 4.176208c.37758093.3912076.98937525.3916069 1.367372-.0000316l4.03091977-4.1763942c.3775978-.3912252.3838182-1.0190815.0160006-1.4001736-.3775061-.39113013-.9877245-.39303641-1.3700683.003106l-2.39538585 2.4818345v-11.6147896l-.00649339-.11662112c-.055753-.49733869-.46370161-.88337888-.95867408-.88337888-.49497246 0-.90292107.38604019-.95867408.88337888l-.00649338.11662112v11.6147896l-2.39518594-2.4816273c-.37913917-.39282218-.98637524-.40056175-1.35419292-.0194697-.37750607.3911302-.37784433 1.0249269.00013556 1.4165479z" fill-rule="evenodd"/></symbol><symbol id="icon-arrow-left" viewBox="0 0 16 16"><path d="m4.46975946 3.28337502-4.17620792 4.03074001c-.39120768.37758093-.39160691.98937525.0000316 1.367372l4.1763942 4.03091977c.39122514.3775978 1.01908149.3838182 1.40017357.0160006.39113012-.3775061.3930364-.9877245-.00310603-1.3700683l-2.48183446-2.39538585h11.61478958l.1166211-.00649339c.4973387-.055753.8833789-.46370161.8833789-.95867408 0-.49497246-.3860402-.90292107-.8833789-.95867408l-.1166211-.00649338h-11.61478958l2.4816273-2.39518594c.39282216-.37913917.40056173-.98637524.01946965-1.35419292-.39113012-.37750607-1.02492687-.37784433-1.41654791.00013556z" fill-rule="evenodd"/></symbol><symbol id="icon-arrow-right" viewBox="0 0 16 16"><path d="m11.5302405 12.716625 4.176208-4.03074003c.3912076-.37758093.3916069-.98937525-.0000316-1.367372l-4.1763942-4.03091981c-.3912252-.37759778-1.0190815-.38381821-1.4001736-.01600053-.39113013.37750607-.39303641.98772445.003106 1.37006824l2.4818345 2.39538588h-11.6147896l-.11662112.00649339c-.49733869.055753-.88337888.46370161-.88337888.95867408 0 .49497246.38604019.90292107.88337888.95867408l.11662112.00649338h11.6147896l-2.4816273 2.39518592c-.39282218.3791392-.40056175.9863753-.0194697 1.3541929.3911302.3775061 1.0249269.3778444 1.4165479-.0001355z" fill-rule="evenodd"/></symbol><symbol id="icon-arrow-sub" viewBox="0 0 16 16"><path d="m7.89692134 4.97190702v7.69043288l-2.44965196-2.4467692c-.38776071-.38730434-1.0088052-.39493519-1.38498697-.0191961-.38609047.3856361-.38643643 1.0105302.00013864 1.3966504l4.12239817 4.1175468c.38616704.3857126 1.01187344.3861062 1.39846576-.0000311l4.12258202-4.1177306c.3861843-.3857298.3925462-1.0047669.0163644-1.380506-.3860905-.38563612-1.0101851-.38751563-1.4012233.0030624l-2.44985643 2.4469734v-8.67638639c0-.54139983-.43698413-.98042709-.98493125-.98159081l-7.89910525-.0043627c-.54516866 0-.98711517.44142642-.98711517.98595351s.44194651.98595351.98711517.98595351z" fill-rule="evenodd"/></symbol><symbol id="icon-arrow-up" viewBox="0 0 16 16"><path d="m12.716625 4.46975946-4.03074003-4.17620792c-.37758093-.39120768-.98937525-.39160691-1.367372.0000316l-4.03091981 4.1763942c-.37759778.39122514-.38381821 1.01908149-.01600053 1.40017357.37750607.39113012.98772445.3930364 1.37006824-.00310603l2.39538588-2.48183446v11.61478958l.00649339.1166211c.055753.4973387.46370161.8833789.95867408.8833789.49497246 0 .90292107-.3860402.95867408-.8833789l.00649338-.1166211v-11.61478958l2.39518592 2.4816273c.3791392.39282216.9863753.40056173 1.3541929.01946965.3775061-.39113012.3778444-1.02492687-.0001355-1.41654791z" fill-rule="evenodd"/></symbol><symbol id="icon-article" viewBox="0 0 18 18"><path d="m13 15v-12.9906311c0-.0073595-.0019884-.0093689.0014977-.0093689l-11.00158888.00087166v13.00506804c0 .5482678.44615281.9940603.99415146.9940603h10.27350412c-.1701701-.2941734-.2675644-.6357129-.2675644-1zm-12 .0059397v-13.00506804c0-.5562408.44704472-1.00087166.99850233-1.00087166h11.00299537c.5510129 0 .9985023.45190985.9985023 1.0093689v2.9906311h3v9.9914698c0 1.1065798-.8927712 2.0085302-1.9940603 2.0085302h-12.01187942c-1.09954652 0-1.99406028-.8927712-1.99406028-1.9940603zm13-9.0059397v9c0 .5522847.4477153 1 1 1s1-.4477153 1-1v-9zm-10-2h7v4h-7zm1 1v2h5v-2zm-1 4h7v1h-7zm0 2h7v1h-7zm0 2h7v1h-7z" fill-rule="evenodd"/></symbol><symbol id="icon-audio" viewBox="0 0 18 18"><path d="m13.0957477 13.5588459c-.195279.1937043-.5119137.193729-.7072234.0000551-.1953098-.193674-.1953346-.5077061-.0000556-.7014104 1.0251004-1.0168342 1.6108711-2.3905226 1.6108711-3.85745208 0-1.46604976-.5850634-2.83898246-1.6090736-3.85566829-.1951894-.19379323-.1950192-.50782531.0003802-.70141028.1953993-.19358497.512034-.19341614.7072234.00037709 1.2094886 1.20083761 1.901635 2.8250555 1.901635 4.55670148 0 1.73268608-.6929822 3.35779608-1.9037571 4.55880738zm2.1233994 2.1025159c-.195234.193749-.5118687.1938462-.7072235.0002171-.1953548-.1936292-.1954528-.5076613-.0002189-.7014104 1.5832215-1.5711805 2.4881302-3.6939808 2.4881302-5.96012998 0-2.26581266-.9046382-4.3883241-2.487443-5.95944795-.1952117-.19377107-.1950777-.50780316.0002993-.70141031s.5120117-.19347426.7072234.00029682c1.7683321 1.75528196 2.7800854 4.12911258 2.7800854 6.66056144 0 2.53182498-1.0120556 4.90597838-2.7808529 6.66132328zm-14.21898205-3.6854911c-.5523759 0-1.00016505-.4441085-1.00016505-.991944v-3.96777631c0-.54783558.44778915-.99194407 1.00016505-.99194407h2.0003301l5.41965617-3.8393633c.44948677-.31842296 1.07413994-.21516983 1.39520191.23062232.12116339.16823446.18629727.36981184.18629727.57655577v12.01603479c0 .5478356-.44778914.9919441-1.00016505.9919441-.20845738 0-.41170538-.0645985-.58133413-.184766l-5.41965617-3.8393633zm0-.991944h2.32084805l5.68047235 4.0241292v-12.01603479l-5.68047235 4.02412928h-2.32084805z" fill-rule="evenodd"/></symbol><symbol id="icon-block" viewBox="0 0 24 24"><path d="m0 0h24v24h-24z" fill-rule="evenodd"/></symbol><symbol id="icon-book" viewBox="0 0 18 18"><path d="m4 13v-11h1v11h11v-11h-13c-.55228475 0-1 .44771525-1 1v10.2675644c.29417337-.1701701.63571286-.2675644 1-.2675644zm12 1h-13c-.55228475 0-1 .4477153-1 1s.44771525 1 1 1h13zm0 3h-13c-1.1045695 0-2-.8954305-2-2v-12c0-1.1045695.8954305-2 2-2h13c.5522847 0 1 .44771525 1 1v14c0 .5522847-.4477153 1-1 1zm-8.5-13h6c.2761424 0 .5.22385763.5.5s-.2238576.5-.5.5h-6c-.27614237 0-.5-.22385763-.5-.5s.22385763-.5.5-.5zm1 2h4c.2761424 0 .5.22385763.5.5s-.2238576.5-.5.5h-4c-.27614237 0-.5-.22385763-.5-.5s.22385763-.5.5-.5z" fill-rule="evenodd"/></symbol><symbol id="icon-broad" viewBox="0 0 24 24"><path d="m9.18274226 7.81v7.7999954l2.48162734-2.4816273c.3928221-.3928221 1.0219731-.4005617 1.4030652-.0194696.3911301.3911301.3914806 1.0249268-.0001404 1.4165479l-4.17620796 4.1762079c-.39120769.3912077-1.02508144.3916069-1.41671995-.0000316l-4.1763942-4.1763942c-.39122514-.3912251-.39767006-1.0190815-.01657798-1.4001736.39113012-.3911301 1.02337106-.3930364 1.41951349.0031061l2.48183446 2.4818344v-8.7999954c0-.54911294.4426881-.99439484.99778758-.99557515l8.00221246-.00442485c.5522847 0 1 .44771525 1 1s-.4477153 1-1 1z" fill-rule="evenodd" transform="matrix(-1 0 0 -1 20.182742 24.805206)"/></symbol><symbol id="icon-calendar" viewBox="0 0 18 18"><path d="m12.5 0c.2761424 0 .5.21505737.5.49047852v.50952148h2c1.1072288 0 2 .89451376 2 2v12c0 1.1072288-.8945138 2-2 2h-12c-1.1072288 0-2-.8945138-2-2v-12c0-1.1072288.89451376-2 2-2h1v1h-1c-.55393837 0-1 .44579254-1 1v3h14v-3c0-.55393837-.4457925-1-1-1h-2v1.50952148c0 .27088381-.2319336.49047852-.5.49047852-.2761424 0-.5-.21505737-.5-.49047852v-3.01904296c0-.27088381.2319336-.49047852.5-.49047852zm3.5 7h-14v8c0 .5539384.44579254 1 1 1h12c.5539384 0 1-.4457925 1-1zm-11 6v1h-1v-1zm3 0v1h-1v-1zm3 0v1h-1v-1zm-6-2v1h-1v-1zm3 0v1h-1v-1zm6 0v1h-1v-1zm-3 0v1h-1v-1zm-3-2v1h-1v-1zm6 0v1h-1v-1zm-3 0v1h-1v-1zm-5.5-9c.27614237 0 .5.21505737.5.49047852v.50952148h5v1h-5v1.50952148c0 .27088381-.23193359.49047852-.5.49047852-.27614237 0-.5-.21505737-.5-.49047852v-3.01904296c0-.27088381.23193359-.49047852.5-.49047852z" fill-rule="evenodd"/></symbol><symbol id="icon-cart" viewBox="0 0 18 18"><path d="m5 14c1.1045695 0 2 .8954305 2 2s-.8954305 2-2 2-2-.8954305-2-2 .8954305-2 2-2zm10 0c1.1045695 0 2 .8954305 2 2s-.8954305 2-2 2-2-.8954305-2-2 .8954305-2 2-2zm-10 1c-.55228475 0-1 .4477153-1 1s.44771525 1 1 1 1-.4477153 1-1-.44771525-1-1-1zm10 0c-.5522847 0-1 .4477153-1 1s.4477153 1 1 1 1-.4477153 1-1-.4477153-1-1-1zm-12.82032249-15c.47691417 0 .88746157.33678127.98070211.80449199l.23823144 1.19501025 13.36277974.00045554c.5522847.00001882.9999659.44774934.9999659 1.00004222 0 .07084994-.0075361.14150708-.022474.2107727l-1.2908094 5.98534344c-.1007861.46742419-.5432548.80388386-1.0571651.80388386h-10.24805106c-.59173366 0-1.07142857.4477153-1.07142857 1 0 .5128358.41361449.9355072.94647737.9932723l.1249512.0067277h10.35933776c.2749512 0 .4979349.2228539.4979349.4978051 0 .2749417-.2227336.4978951-.4976753.4980063l-10.35959736.0041886c-1.18346732 0-2.14285714-.8954305-2.14285714-2 0-.6625717.34520317-1.24989198.87690425-1.61383592l-1.63768102-8.19004794c-.01312273-.06561364-.01950005-.131011-.0196107-.19547395l-1.71961253-.00064219c-.27614237 0-.5-.22385762-.5-.5 0-.27614237.22385763-.5.5-.5zm14.53193359 2.99950224h-13.11300004l1.20580469 6.02530174c.11024034-.0163252.22327998-.02480398.33844139-.02480398h10.27064786z"/></symbol><symbol id="icon-chevron-less" viewBox="0 0 10 10"><path d="m5.58578644 4-3.29289322-3.29289322c-.39052429-.39052429-.39052429-1.02368927 0-1.41421356s1.02368927-.39052429 1.41421356 0l4 4c.39052429.39052429.39052429 1.02368927 0 1.41421356l-4 4c-.39052429.39052429-1.02368927.39052429-1.41421356 0s-.39052429-1.02368927 0-1.41421356z" fill-rule="evenodd" transform="matrix(0 -1 -1 0 9 9)"/></symbol><symbol id="icon-chevron-more" viewBox="0 0 10 10"><path d="m5.58578644 6-3.29289322-3.29289322c-.39052429-.39052429-.39052429-1.02368927 0-1.41421356s1.02368927-.39052429 1.41421356 0l4 4c.39052429.39052429.39052429 1.02368927 0 1.41421356l-4 4.00000002c-.39052429.3905243-1.02368927.3905243-1.41421356 0s-.39052429-1.02368929 0-1.41421358z" fill-rule="evenodd" transform="matrix(0 1 -1 0 11 1)"/></symbol><symbol id="icon-chevron-right" viewBox="0 0 10 10"><path d="m5.96738168 4.70639573 2.39518594-2.41447274c.37913917-.38219212.98637524-.38972225 1.35419292-.01894278.37750606.38054586.37784436.99719163-.00013556 1.37821513l-4.03074001 4.06319683c-.37758093.38062133-.98937525.38100976-1.367372-.00003075l-4.03091981-4.06337806c-.37759778-.38063832-.38381821-.99150444-.01600053-1.3622839.37750607-.38054587.98772445-.38240057 1.37006824.00302197l2.39538588 2.4146743.96295325.98624457z" fill-rule="evenodd" transform="matrix(0 -1 1 0 0 10)"/></symbol><symbol id="icon-circle-fill" viewBox="0 0 16 16"><path d="m8 14c-3.3137085 0-6-2.6862915-6-6s2.6862915-6 6-6 6 2.6862915 6 6-2.6862915 6-6 6z" fill-rule="evenodd"/></symbol><symbol id="icon-circle" viewBox="0 0 16 16"><path d="m8 12c2.209139 0 4-1.790861 4-4s-1.790861-4-4-4-4 1.790861-4 4 1.790861 4 4 4zm0 2c-3.3137085 0-6-2.6862915-6-6s2.6862915-6 6-6 6 2.6862915 6 6-2.6862915 6-6 6z" fill-rule="evenodd"/></symbol><symbol id="icon-citation" viewBox="0 0 18 18"><path d="m8.63593473 5.99995183c2.20913897 0 3.99999997 1.79084375 3.99999997 3.99996146 0 1.40730761-.7267788 2.64486871-1.8254829 3.35783281 1.6240224.6764218 2.8754442 2.0093871 3.4610603 3.6412466l-1.0763845.000006c-.5310008-1.2078237-1.5108121-2.1940153-2.7691712-2.7181346l-.79002167-.329052v-1.023992l.63016577-.4089232c.8482885-.5504661 1.3698342-1.4895187 1.3698342-2.51898361 0-1.65683828-1.3431457-2.99996146-2.99999997-2.99996146-1.65685425 0-3 1.34312318-3 2.99996146 0 1.02946491.52154569 1.96851751 1.36983419 2.51898361l.63016581.4089232v1.023992l-.79002171.329052c-1.25835905.5241193-2.23817037 1.5103109-2.76917113 2.7181346l-1.07638453-.000006c.58561612-1.6318595 1.8370379-2.9648248 3.46106024-3.6412466-1.09870405-.7129641-1.82548287-1.9505252-1.82548287-3.35783281 0-2.20911771 1.790861-3.99996146 4-3.99996146zm7.36897597-4.99995183c1.1018574 0 1.9950893.89353404 1.9950893 2.00274083v5.994422c0 1.10608317-.8926228 2.00274087-1.9950893 2.00274087l-3.0049107-.0009037v-1l3.0049107.00091329c.5490631 0 .9950893-.44783123.9950893-1.00275046v-5.994422c0-.55646537-.4450595-1.00275046-.9950893-1.00275046h-14.00982141c-.54906309 0-.99508929.44783123-.99508929 1.00275046v5.9971821c0 .66666024.33333333.99999036 1 .99999036l2-.00091329v1l-2 .0009037c-1 0-2-.99999041-2-1.99998077v-5.9971821c0-1.10608322.8926228-2.00274083 1.99508929-2.00274083zm-8.5049107 2.9999711c.27614237 0 .5.22385547.5.5 0 .2761349-.22385763.5-.5.5h-4c-.27614237 0-.5-.2238651-.5-.5 0-.27614453.22385763-.5.5-.5zm3 0c.2761424 0 .5.22385547.5.5 0 .2761349-.2238576.5-.5.5h-1c-.27614237 0-.5-.2238651-.5-.5 0-.27614453.22385763-.5.5-.5zm4 0c.2761424 0 .5.22385547.5.5 0 .2761349-.2238576.5-.5.5h-2c-.2761424 0-.5-.2238651-.5-.5 0-.27614453.2238576-.5.5-.5z" fill-rule="evenodd"/></symbol><symbol id="icon-close" viewBox="0 0 16 16"><path d="m2.29679575 12.2772478c-.39658757.3965876-.39438847 1.0328109-.00062148 1.4265779.39651227.3965123 1.03246768.3934888 1.42657791-.0006214l4.27724782-4.27724787 4.2772478 4.27724787c.3965876.3965875 1.0328109.3943884 1.4265779.0006214.3965123-.3965122.3934888-1.0324677-.0006214-1.4265779l-4.27724787-4.2772478 4.27724787-4.27724782c.3965875-.39658757.3943884-1.03281091.0006214-1.42657791-.3965122-.39651226-1.0324677-.39348875-1.4265779.00062148l-4.2772478 4.27724782-4.27724782-4.27724782c-.39658757-.39658757-1.03281091-.39438847-1.42657791-.00062148-.39651226.39651227-.39348875 1.03246768.00062148 1.42657791l4.27724782 4.27724782z" fill-rule="evenodd"/></symbol><symbol id="icon-collections" viewBox="0 0 18 18"><path d="m15 4c1.1045695 0 2 .8954305 2 2v9c0 1.1045695-.8954305 2-2 2h-8c-1.1045695 0-2-.8954305-2-2h1c0 .5128358.38604019.9355072.88337887.9932723l.11662113.0067277h8c.5128358 0 .9355072-.3860402.9932723-.8833789l.0067277-.1166211v-9c0-.51283584-.3860402-.93550716-.8833789-.99327227l-.1166211-.00672773h-1v-1zm-4-3c1.1045695 0 2 .8954305 2 2v9c0 1.1045695-.8954305 2-2 2h-8c-1.1045695 0-2-.8954305-2-2v-9c0-1.1045695.8954305-2 2-2zm0 1h-8c-.51283584 0-.93550716.38604019-.99327227.88337887l-.00672773.11662113v9c0 .5128358.38604019.9355072.88337887.9932723l.11662113.0067277h8c.5128358 0 .9355072-.3860402.9932723-.8833789l.0067277-.1166211v-9c0-.51283584-.3860402-.93550716-.8833789-.99327227zm-1.5 7c.27614237 0 .5.22385763.5.5s-.22385763.5-.5.5h-5c-.27614237 0-.5-.22385763-.5-.5s.22385763-.5.5-.5zm0-2c.27614237 0 .5.22385763.5.5s-.22385763.5-.5.5h-5c-.27614237 0-.5-.22385763-.5-.5s.22385763-.5.5-.5zm0-2c.27614237 0 .5.22385763.5.5s-.22385763.5-.5.5h-5c-.27614237 0-.5-.22385763-.5-.5s.22385763-.5.5-.5z" fill-rule="evenodd"/></symbol><symbol id="icon-compare" viewBox="0 0 18 18"><path d="m12 3c3.3137085 0 6 2.6862915 6 6s-2.6862915 6-6 6c-1.0928452 0-2.11744941-.2921742-2.99996061-.8026704-.88181407.5102749-1.90678042.8026704-3.00003939.8026704-3.3137085 0-6-2.6862915-6-6s2.6862915-6 6-6c1.09325897 0 2.11822532.29239547 3.00096303.80325037.88158756-.51107621 1.90619177-.80325037 2.99903697-.80325037zm-6 1c-2.76142375 0-5 2.23857625-5 5 0 2.7614237 2.23857625 5 5 5 .74397391 0 1.44999672-.162488 2.08451611-.4539116-1.27652344-1.1000812-2.08451611-2.7287264-2.08451611-4.5460884s.80799267-3.44600721 2.08434391-4.5463015c-.63434719-.29121054-1.34037-.4536985-2.08434391-.4536985zm6 0c-.7439739 0-1.4499967.16248796-2.08451611.45391156 1.27652341 1.10008123 2.08451611 2.72872644 2.08451611 4.54608844s-.8079927 3.4460072-2.08434391 4.5463015c.63434721.2912105 1.34037001.4536985 2.08434391.4536985 2.7614237 0 5-2.2385763 5-5 0-2.76142375-2.2385763-5-5-5zm-1.4162763 7.0005324h-3.16744736c.15614659.3572676.35283837.6927622.58425872 1.0006671h1.99892988c.23142036-.3079049.42811216-.6433995.58425876-1.0006671zm.4162763-2.0005324h-4c0 .34288501.0345146.67770871.10025909 1.0011864h3.79948181c.0657445-.32347769.1002591-.65830139.1002591-1.0011864zm-.4158423-1.99953894h-3.16831543c-.13859957.31730812-.24521946.651783-.31578599.99935097h3.79988742c-.0705665-.34756797-.1771864-.68204285-.315786-.99935097zm-1.58295822-1.999926-.08316107.06199199c-.34550042.27081213-.65446126.58611297-.91825862.93727862h2.00044041c-.28418626-.37830727-.6207872-.71499149-.99902072-.99927061z" fill-rule="evenodd"/></symbol><symbol id="icon-download-file" viewBox="0 0 18 18"><path d="m10.0046024 0c.5497429 0 1.3179837.32258606 1.707238.71184039l4.5763192 4.57631922c.3931386.39313859.7118404 1.16760135.7118404 1.71431368v8.98899651c0 1.1092806-.8945138 2.0085302-1.9940603 2.0085302h-12.01187942c-1.10128908 0-1.99406028-.8926228-1.99406028-1.9950893v-14.00982141c0-1.10185739.88743329-1.99508929 1.99961498-1.99508929zm0 1h-7.00498742c-.55709576 0-.99961498.44271433-.99961498.99508929v14.00982141c0 .5500396.44491393.9950893.99406028.9950893h12.01187942c.5463747 0 .9940603-.4506622.9940603-1.0085302v-8.98899651c0-.28393444-.2150684-.80332809-.4189472-1.0072069l-4.5763192-4.57631922c-.2038461-.20384606-.718603-.41894717-1.0001312-.41894717zm-1.5046024 4c.27614237 0 .5.21637201.5.49209595v6.14827645l1.7462789-1.77990922c.1933927-.1971171.5125222-.19455839.7001689-.0069117.1932998.19329992.1910058.50899492-.0027774.70277812l-2.59089271 2.5908927c-.19483374.1948337-.51177825.1937771-.70556873-.0000133l-2.59099079-2.5909908c-.19484111-.1948411-.19043735-.5151448-.00279066-.70279146.19329987-.19329987.50465175-.19237083.70018565.00692852l1.74638684 1.78001764v-6.14827695c0-.27177709.23193359-.49209595.5-.49209595z" fill-rule="evenodd"/></symbol><symbol id="icon-download" viewBox="0 0 16 16"><path d="m12.9975267 12.999368c.5467123 0 1.0024733.4478567 1.0024733 1.000316 0 .5563109-.4488226 1.000316-1.0024733 1.000316h-9.99505341c-.54671233 0-1.00247329-.4478567-1.00247329-1.000316 0-.5563109.44882258-1.000316 1.00247329-1.000316zm-4.9975267-11.999368c.55228475 0 1 .44497754 1 .99589209v6.80214418l2.4816273-2.48241149c.3928222-.39294628 1.0219732-.4006883 1.4030652-.01947579.3911302.39125371.3914806 1.02525073-.0001404 1.41699553l-4.17620792 4.17752758c-.39120769.3913313-1.02508144.3917306-1.41671995-.0000316l-4.17639421-4.17771394c-.39122513-.39134876-.39767006-1.01940351-.01657797-1.40061601.39113012-.39125372 1.02337105-.3931606 1.41951349.00310701l2.48183446 2.48261871v-6.80214418c0-.55001601.44386482-.99589209 1-.99589209z" fill-rule="evenodd"/></symbol><symbol id="icon-editors" viewBox="0 0 18 18"><path d="m8.72592184 2.54588137c-.48811714-.34391207-1.08343326-.54588137-1.72592184-.54588137-1.65685425 0-3 1.34314575-3 3 0 1.02947485.5215457 1.96853646 1.3698342 2.51900785l.6301658.40892721v1.02400182l-.79002171.32905522c-1.93395773.8055207-3.20997829 2.7024791-3.20997829 4.8180274v.9009805h-1v-.9009805c0-2.5479714 1.54557359-4.79153984 3.82548288-5.7411543-1.09870406-.71297106-1.82548288-1.95054399-1.82548288-3.3578652 0-2.209139 1.790861-4 4-4 1.09079823 0 2.07961816.43662103 2.80122451 1.1446278-.37707584.09278571-.7373238.22835063-1.07530267.40125357zm-2.72592184 14.45411863h-1v-.9009805c0-2.5479714 1.54557359-4.7915398 3.82548288-5.7411543-1.09870406-.71297106-1.82548288-1.95054399-1.82548288-3.3578652 0-2.209139 1.790861-4 4-4s4 1.790861 4 4c0 1.40732121-.7267788 2.64489414-1.8254829 3.3578652 2.2799093.9496145 3.8254829 3.1931829 3.8254829 5.7411543v.9009805h-1v-.9009805c0-2.1155483-1.2760206-4.0125067-3.2099783-4.8180274l-.7900217-.3290552v-1.02400184l.6301658-.40892721c.8482885-.55047139 1.3698342-1.489533 1.3698342-2.51900785 0-1.65685425-1.3431458-3-3-3-1.65685425 0-3 1.34314575-3 3 0 1.02947485.5215457 1.96853646 1.3698342 2.51900785l.6301658.40892721v1.02400184l-.79002171.3290552c-1.93395773.8055207-3.20997829 2.7024791-3.20997829 4.8180274z" fill-rule="evenodd"/></symbol><symbol id="icon-email" viewBox="0 0 18 18"><path d="m16.0049107 2c1.1018574 0 1.9950893.89706013 1.9950893 2.00585866v9.98828264c0 1.1078052-.8926228 2.0058587-1.9950893 2.0058587h-14.00982141c-1.10185739 0-1.99508929-.8970601-1.99508929-2.0058587v-9.98828264c0-1.10780515.8926228-2.00585866 1.99508929-2.00585866zm0 1h-14.00982141c-.54871518 0-.99508929.44887827-.99508929 1.00585866v9.98828264c0 .5572961.44630695 1.0058587.99508929 1.0058587h14.00982141c.5487152 0 .9950893-.4488783.9950893-1.0058587v-9.98828264c0-.55729607-.446307-1.00585866-.9950893-1.00585866zm-.0049107 2.55749512v1.44250488l-7 4-7-4v-1.44250488l7 4z" fill-rule="evenodd"/></symbol><symbol id="icon-error" viewBox="0 0 18 18"><path d="m9 0c4.9705627 0 9 4.02943725 9 9 0 4.9705627-4.0294373 9-9 9-4.97056275 0-9-4.0294373-9-9 0-4.97056275 4.02943725-9 9-9zm2.8630343 4.71100931-2.8630343 2.86303426-2.86303426-2.86303426c-.39658757-.39658757-1.03281091-.39438847-1.4265779-.00062147-.39651227.39651226-.39348876 1.03246767.00062147 1.4265779l2.86303426 2.86303426-2.86303426 2.8630343c-.39658757.3965875-.39438847 1.0328109-.00062147 1.4265779.39651226.3965122 1.03246767.3934887 1.4265779-.0006215l2.86303426-2.8630343 2.8630343 2.8630343c.3965875.3965876 1.0328109.3943885 1.4265779.0006215.3965122-.3965123.3934887-1.0324677-.0006215-1.4265779l-2.8630343-2.8630343 2.8630343-2.86303426c.3965876-.39658757.3943885-1.03281091.0006215-1.4265779-.3965123-.39651227-1.0324677-.39348876-1.4265779.00062147z" fill-rule="evenodd"/></symbol><symbol id="icon-ethics" viewBox="0 0 18 18"><path d="m6.76384967 1.41421356.83301651-.8330165c.77492941-.77492941 2.03133823-.77492941 2.80626762 0l.8330165.8330165c.3750728.37507276.8837806.58578644 1.4142136.58578644h1.3496361c1.1045695 0 2 .8954305 2 2v1.34963611c0 .53043298.2107137 1.03914081.5857864 1.41421356l.8330165.83301651c.7749295.77492941.7749295 2.03133823 0 2.80626762l-.8330165.8330165c-.3750727.3750728-.5857864.8837806-.5857864 1.4142136v1.3496361c0 1.1045695-.8954305 2-2 2h-1.3496361c-.530433 0-1.0391408.2107137-1.4142136.5857864l-.8330165.8330165c-.77492939.7749295-2.03133821.7749295-2.80626762 0l-.83301651-.8330165c-.37507275-.3750727-.88378058-.5857864-1.41421356-.5857864h-1.34963611c-1.1045695 0-2-.8954305-2-2v-1.3496361c0-.530433-.21071368-1.0391408-.58578644-1.4142136l-.8330165-.8330165c-.77492941-.77492939-.77492941-2.03133821 0-2.80626762l.8330165-.83301651c.37507276-.37507275.58578644-.88378058.58578644-1.41421356v-1.34963611c0-1.1045695.8954305-2 2-2h1.34963611c.53043298 0 1.03914081-.21071368 1.41421356-.58578644zm-1.41421356 1.58578644h-1.34963611c-.55228475 0-1 .44771525-1 1v1.34963611c0 .79564947-.31607052 1.55871121-.87867966 2.12132034l-.8330165.83301651c-.38440512.38440512-.38440512 1.00764896 0 1.39205408l.8330165.83301646c.56260914.5626092.87867966 1.3256709.87867966 2.1213204v1.3496361c0 .5522847.44771525 1 1 1h1.34963611c.79564947 0 1.55871121.3160705 2.12132034.8786797l.83301651.8330165c.38440512.3844051 1.00764896.3844051 1.39205408 0l.83301646-.8330165c.5626092-.5626092 1.3256709-.8786797 2.1213204-.8786797h1.3496361c.5522847 0 1-.4477153 1-1v-1.3496361c0-.7956495.3160705-1.5587112.8786797-2.1213204l.8330165-.83301646c.3844051-.38440512.3844051-1.00764896 0-1.39205408l-.8330165-.83301651c-.5626092-.56260913-.8786797-1.32567087-.8786797-2.12132034v-1.34963611c0-.55228475-.4477153-1-1-1h-1.3496361c-.7956495 0-1.5587112-.31607052-2.1213204-.87867966l-.83301646-.8330165c-.38440512-.38440512-1.00764896-.38440512-1.39205408 0l-.83301651.8330165c-.56260913.56260914-1.32567087.87867966-2.12132034.87867966zm3.58698944 11.4960218c-.02081224.002155-.04199226.0030286-.06345763.002542-.98766446-.0223875-1.93408568-.3063547-2.75885125-.8155622-.23496767-.1450683-.30784554-.4531483-.16277726-.688116.14506827-.2349677.45314827-.3078455.68811595-.1627773.67447084.4164161 1.44758575.6483839 2.25617384.6667123.01759529.0003988.03495764.0017019.05204365.0038639.01713363-.0017748.03452416-.0026845.05212715-.0026845 2.4852814 0 4.5-2.0147186 4.5-4.5 0-1.04888973-.3593547-2.04134635-1.0074477-2.83787157-.1742817-.21419731-.1419238-.5291218.0722736-.70340353.2141973-.17428173.5291218-.14192375.7034035.07227357.7919032.97327203 1.2317706 2.18808682 1.2317706 3.46900153 0 3.0375661-2.4624339 5.5-5.5 5.5-.02146768 0-.04261937-.0013529-.06337445-.0039782zm1.57975095-10.78419583c.2654788.07599731.419084.35281842.3430867.61829728-.0759973.26547885-.3528185.419084-.6182973.3430867-.37560116-.10752146-.76586237-.16587951-1.15568824-.17249193-2.5587807-.00064534-4.58547766 2.00216524-4.58547766 4.49928198 0 .62691557.12797645 1.23496.37274865 1.7964426.11035133.2531347-.0053975.5477984-.25853224.6581497-.25313473.1103514-.54779841-.0053975-.65814974-.2585322-.29947131-.6869568-.45606667-1.43097603-.45606667-2.1960601 0-3.05211432 2.47714695-5.50006595 5.59399617-5.49921198.48576182.00815502.96289603.0795037 1.42238033.21103795zm-1.9766658 6.41091303 2.69835-2.94655317c.1788432-.21040373.4943901-.23598862.7047939-.05714545.2104037.17884318.2359886.49439014.0571454.70479387l-3.01637681 3.34277395c-.18039088.1999106-.48669547.2210637-.69285412.0478478l-1.93095347-1.62240047c-.21213845-.17678204-.24080048-.49206439-.06401844-.70420284.17678204-.21213844.49206439-.24080048.70420284-.06401844z" fill-rule="evenodd"/></symbol><symbol id="icon-expand"><path d="M7.498 11.918a.997.997 0 0 0-.003-1.411.995.995 0 0 0-1.412-.003l-4.102 4.102v-3.51A1 1 0 0 0 .98 10.09.992.992 0 0 0 0 11.092V17c0 .554.448 1.002 1.002 1.002h5.907c.554 0 1.002-.45 1.002-1.003 0-.539-.45-.978-1.006-.978h-3.51zm3.005-5.835a.997.997 0 0 0 .003 1.412.995.995 0 0 0 1.411.003l4.103-4.103v3.51a1 1 0 0 0 1.001 1.006A.992.992 0 0 0 18 6.91V1.002A1 1 0 0 0 17 0h-5.907a1.003 1.003 0 0 0-1.002 1.003c0 .539.45.978 1.006.978h3.51z" fill-rule="evenodd"/></symbol><symbol id="icon-explore" viewBox="0 0 18 18"><path d="m9 17c4.418278 0 8-3.581722 8-8s-3.581722-8-8-8-8 3.581722-8 8 3.581722 8 8 8zm0 1c-4.97056275 0-9-4.0294373-9-9 0-4.97056275 4.02943725-9 9-9 4.9705627 0 9 4.02943725 9 9 0 4.9705627-4.0294373 9-9 9zm0-2.5c-.27614237 0-.5-.2238576-.5-.5s.22385763-.5.5-.5c2.969509 0 5.400504-2.3575119 5.497023-5.31714844.0090007-.27599565.2400359-.49243782.5160315-.48343711.2759957.0090007.4924378.2400359.4834371.51603155-.114093 3.4985237-2.9869632 6.284554-6.4964916 6.284554zm-.29090657-12.99359748c.27587424-.01216621.50937715.20161139.52154336.47748563.01216621.27587423-.20161139.50937715-.47748563.52154336-2.93195733.12930094-5.25315116 2.54886451-5.25315116 5.49456849 0 .27614237-.22385763.5-.5.5s-.5-.22385763-.5-.5c0-3.48142406 2.74307146-6.34074398 6.20909343-6.49359748zm1.13784138 8.04763908-1.2004882-1.20048821c-.19526215-.19526215-.19526215-.51184463 0-.70710678s.51184463-.19526215.70710678 0l1.20048821 1.2004882 1.6006509-4.00162734-4.50670359 1.80268144-1.80268144 4.50670359zm4.10281269-6.50378907-2.6692597 6.67314927c-.1016411.2541026-.3029834.4554449-.557086.557086l-6.67314927 2.6692597 2.66925969-6.67314926c.10164107-.25410266.30298336-.45544495.55708602-.55708602z" fill-rule="evenodd"/></symbol><symbol id="icon-filter" viewBox="0 0 16 16"><path d="m14.9738641 0c.5667192 0 1.0261359.4477136 1.0261359 1 0 .24221858-.0902161.47620768-.2538899.65849851l-5.6938314 6.34147206v5.49997973c0 .3147562-.1520673.6111434-.4104543.7999971l-2.05227171 1.4999945c-.45337535.3313696-1.09655869.2418269-1.4365902-.1999993-.13321514-.1730955-.20522717-.3836284-.20522717-.5999978v-6.99997423l-5.69383133-6.34147206c-.3731872-.41563511-.32996891-1.0473954.09653074-1.41107611.18705584-.15950448.42716133-.2474224.67571519-.2474224zm-5.9218641 8.5h-2.105v6.491l.01238459.0070843.02053271.0015705.01955278-.0070558 2.0532976-1.4990996zm-8.02585008-7.5-.01564945.00240169 5.83249953 6.49759831h2.313l5.836-6.499z"/></symbol><symbol id="icon-home" viewBox="0 0 18 18"><path d="m9 5-6 6v5h4v-4h4v4h4v-5zm7 6.5857864v4.4142136c0 .5522847-.4477153 1-1 1h-5v-4h-2v4h-5c-.55228475 0-1-.4477153-1-1v-4.4142136c-.25592232 0-.51184464-.097631-.70710678-.2928932l-.58578644-.5857864c-.39052429-.3905243-.39052429-1.02368929 0-1.41421358l8.29289322-8.29289322 8.2928932 8.29289322c.3905243.39052429.3905243 1.02368928 0 1.41421358l-.5857864.5857864c-.1952622.1952622-.4511845.2928932-.7071068.2928932zm-7-9.17157284-7.58578644 7.58578644.58578644.5857864 7-6.99999996 7 6.99999996.5857864-.5857864z" fill-rule="evenodd"/></symbol><symbol id="icon-image" viewBox="0 0 18 18"><path d="m10.0046024 0c.5497429 0 1.3179837.32258606 1.707238.71184039l4.5763192 4.57631922c.3931386.39313859.7118404 1.16760135.7118404 1.71431368v8.98899651c0 1.1092806-.8945138 2.0085302-1.9940603 2.0085302h-12.01187942c-1.10128908 0-1.99406028-.8926228-1.99406028-1.9950893v-14.00982141c0-1.10185739.88743329-1.99508929 1.99961498-1.99508929zm-3.49645283 10.1752453-3.89407257 6.7495552c.11705545.048464.24538859.0751995.37998328.0751995h10.60290092l-2.4329715-4.2154691-1.57494129 2.7288098zm8.49779013 6.8247547c.5463747 0 .9940603-.4506622.9940603-1.0085302v-8.98899651c0-.28393444-.2150684-.80332809-.4189472-1.0072069l-4.5763192-4.57631922c-.2038461-.20384606-.718603-.41894717-1.0001312-.41894717h-7.00498742c-.55709576 0-.99961498.44271433-.99961498.99508929v13.98991071l4.50814957-7.81026689 3.08089884 5.33809539 1.57494129-2.7288097 3.5875735 6.2159812zm-3.0059397-11c1.1045695 0 2 .8954305 2 2s-.8954305 2-2 2-2-.8954305-2-2 .8954305-2 2-2zm0 1c-.5522847 0-1 .44771525-1 1s.4477153 1 1 1 1-.44771525 1-1-.4477153-1-1-1z" fill-rule="evenodd"/></symbol><symbol id="icon-info" viewBox="0 0 18 18"><path d="m9 0c4.9705627 0 9 4.02943725 9 9 0 4.9705627-4.0294373 9-9 9-4.97056275 0-9-4.0294373-9-9 0-4.97056275 4.02943725-9 9-9zm0 7h-1.5l-.11662113.00672773c-.49733868.05776511-.88337887.48043643-.88337887.99327227 0 .47338693.32893365.86994729.77070917.97358929l.1126697.01968298.11662113.00672773h.5v3h-.5l-.11662113.0067277c-.42082504.0488782-.76196299.3590206-.85696816.7639815l-.01968298.1126697-.00672773.1166211.00672773.1166211c.04887817.4208251.35902055.761963.76398144.8569682l.1126697.019683.11662113.0067277h3l.1166211-.0067277c.4973387-.0577651.8833789-.4804365.8833789-.9932723 0-.4733869-.3289337-.8699473-.7707092-.9735893l-.1126697-.019683-.1166211-.0067277h-.5v-4l-.00672773-.11662113c-.04887817-.42082504-.35902055-.76196299-.76398144-.85696816l-.1126697-.01968298zm0-3.25c-.69035594 0-1.25.55964406-1.25 1.25s.55964406 1.25 1.25 1.25 1.25-.55964406 1.25-1.25-.55964406-1.25-1.25-1.25z" fill-rule="evenodd"/></symbol><symbol id="icon-institution" viewBox="0 0 18 18"><path d="m7 16.9998189v-2.0003623h4v2.0003623h2v-3.0005434h-8v3.0005434zm-3-10.00181122h-1.52632364c-.27614237 0-.5-.22389817-.5-.50009056 0-.13995446.05863589-.27350497.16166338-.36820841l1.23156713-1.13206327h-2.36690687v12.00217346h3v-2.0003623h-3v-1.0001811h3v-1.0001811h1v-4.00072448h-1zm10 0v2.00036224h-1v4.00072448h1v1.0001811h3v1.0001811h-3v2.0003623h3v-12.00217346h-2.3695309l1.2315671 1.13206327c.2033191.186892.2166633.50325042.0298051.70660631-.0946863.10304615-.2282126.16169266-.3681417.16169266zm3-3.00054336c.5522847 0 1 .44779634 1 1.00018112v13.00235456h-18v-13.00235456c0-.55238478.44771525-1.00018112 1-1.00018112h3.45499992l4.20535144-3.86558216c.19129876-.17584288.48537447-.17584288.67667324 0l4.2053514 3.86558216zm-4 3.00054336h-8v1.00018112h8zm-2 6.00108672h1v-4.00072448h-1zm-1 0v-4.00072448h-2v4.00072448zm-3 0v-4.00072448h-1v4.00072448zm8-4.00072448c.5522847 0 1 .44779634 1 1.00018112v2.00036226h-2v-2.00036226c0-.55238478.4477153-1.00018112 1-1.00018112zm-12 0c.55228475 0 1 .44779634 1 1.00018112v2.00036226h-2v-2.00036226c0-.55238478.44771525-1.00018112 1-1.00018112zm5.99868798-7.81907007-5.24205601 4.81852671h10.48411203zm.00131202 3.81834559c-.55228475 0-1-.44779634-1-1.00018112s.44771525-1.00018112 1-1.00018112 1 .44779634 1 1.00018112-.44771525 1.00018112-1 1.00018112zm-1 11.00199236v1.0001811h2v-1.0001811z" fill-rule="evenodd"/></symbol><symbol id="icon-location" viewBox="0 0 18 18"><path d="m9.39521328 16.2688008c.79596342-.7770119 1.59208152-1.6299956 2.33285652-2.5295081 1.4020032-1.7024324 2.4323601-3.3624519 2.9354918-4.871847.2228715-.66861448.3364384-1.29323246.3364384-1.8674457 0-3.3137085-2.6862915-6-6-6-3.36356866 0-6 2.60156856-6 6 0 .57421324.11356691 1.19883122.3364384 1.8674457.50313169 1.5093951 1.53348863 3.1694146 2.93549184 4.871847.74077492.8995125 1.53689309 1.7524962 2.33285648 2.5295081.13694479.1336842.26895677.2602648.39521328.3793207.12625651-.1190559.25826849-.2456365.39521328-.3793207zm-.39521328 1.7311992s-7-6-7-11c0-4 3.13400675-7 7-7 3.8659932 0 7 3.13400675 7 7 0 5-7 11-7 11zm0-8c-1.65685425 0-3-1.34314575-3-3s1.34314575-3 3-3c1.6568542 0 3 1.34314575 3 3s-1.3431458 3-3 3zm0-1c1.1045695 0 2-.8954305 2-2s-.8954305-2-2-2-2 .8954305-2 2 .8954305 2 2 2z" fill-rule="evenodd"/></symbol><symbol id="icon-minus" viewBox="0 0 16 16"><path d="m2.00087166 7h11.99825664c.5527662 0 1.0008717.44386482 1.0008717 1 0 .55228475-.4446309 1-1.0008717 1h-11.99825664c-.55276616 0-1.00087166-.44386482-1.00087166-1 0-.55228475.44463086-1 1.00087166-1z" fill-rule="evenodd"/></symbol><symbol id="icon-newsletter" viewBox="0 0 18 18"><path d="m9 11.8482489 2-1.1428571v-1.7053918h-4v1.7053918zm-3-1.7142857v-2.1339632h6v2.1339632l3-1.71428574v-6.41967746h-12v6.41967746zm10-5.3839632 1.5299989.95624934c.2923814.18273835.4700011.50320827.4700011.8479983v8.44575236c0 1.1045695-.8954305 2-2 2h-14c-1.1045695 0-2-.8954305-2-2v-8.44575236c0-.34479003.1776197-.66525995.47000106-.8479983l1.52999894-.95624934v-2.75c0-.55228475.44771525-1 1-1h12c.5522847 0 1 .44771525 1 1zm0 1.17924764v3.07075236l-7 4-7-4v-3.07075236l-1 .625v8.44575236c0 .5522847.44771525 1 1 1h14c.5522847 0 1-.4477153 1-1v-8.44575236zm-10-1.92924764h6v1h-6zm-1 2h8v1h-8z" fill-rule="evenodd"/></symbol><symbol id="icon-orcid" viewBox="0 0 18 18"><path d="m9 1c4.418278 0 8 3.581722 8 8s-3.581722 8-8 8-8-3.581722-8-8 3.581722-8 8-8zm-2.90107518 5.2732337h-1.41865256v7.1712107h1.41865256zm4.55867178.02508949h-2.99247027v7.14612121h2.91062487c.7673039 0 1.4476365-.1483432 2.0410182-.445034s1.0511995-.7152915 1.3734671-1.2558144c.3222677-.540523.4833991-1.1603247.4833991-1.85942385 0-.68545815-.1602789-1.30270225-.4808414-1.85175082-.3205625-.54904856-.7707074-.97532211-1.3504481-1.27883343-.5797408-.30351132-1.2413173-.45526471-1.9847495-.45526471zm-.1892674 1.07933542c.7877654 0 1.4143875.22336734 1.8798852.67010873.4654977.44674138.698243 1.05546001.698243 1.82617415 0 .74343221-.2310402 1.34447791-.6931277 1.80315511-.4620874.4586773-1.0750688.6880124-1.8389625.6880124h-1.46810075v-4.98745039zm-5.08652545-3.71099194c-.21825533 0-.410525.08444276-.57681478.25333081-.16628977.16888806-.24943341.36245684-.24943341.58071218 0 .22345188.08314364.41961891.24943341.58850696.16628978.16888806.35855945.25333082.57681478.25333082.233845 0 .43390938-.08314364.60019916-.24943342.16628978-.16628977.24943342-.36375592.24943342-.59240436 0-.233845-.08314364-.43131115-.24943342-.59240437s-.36635416-.24163862-.60019916-.24163862z" fill-rule="evenodd"/></symbol><symbol id="icon-plus" viewBox="0 0 16 16"><path d="m2.00087166 7h4.99912834v-4.99912834c0-.55276616.44386482-1.00087166 1-1.00087166.55228475 0 1 .44463086 1 1.00087166v4.99912834h4.9991283c.5527662 0 1.0008717.44386482 1.0008717 1 0 .55228475-.4446309 1-1.0008717 1h-4.9991283v4.9991283c0 .5527662-.44386482 1.0008717-1 1.0008717-.55228475 0-1-.4446309-1-1.0008717v-4.9991283h-4.99912834c-.55276616 0-1.00087166-.44386482-1.00087166-1 0-.55228475.44463086-1 1.00087166-1z" fill-rule="evenodd"/></symbol><symbol id="icon-print" viewBox="0 0 18 18"><path d="m16.0049107 5h-14.00982141c-.54941618 0-.99508929.4467783-.99508929.99961498v6.00077002c0 .5570958.44271433.999615.99508929.999615h1.00491071v-3h12v3h1.0049107c.5494162 0 .9950893-.4467783.9950893-.999615v-6.00077002c0-.55709576-.4427143-.99961498-.9950893-.99961498zm-2.0049107-1v-2.00208688c0-.54777062-.4519464-.99791312-1.0085302-.99791312h-7.9829396c-.55661731 0-1.0085302.44910695-1.0085302.99791312v2.00208688zm1 10v2.0018986c0 1.103521-.9019504 1.9981014-2.0085302 1.9981014h-7.9829396c-1.1092806 0-2.0085302-.8867064-2.0085302-1.9981014v-2.0018986h-1.00491071c-1.10185739 0-1.99508929-.8874333-1.99508929-1.999615v-6.00077002c0-1.10435686.8926228-1.99961498 1.99508929-1.99961498h1.00491071v-2.00208688c0-1.10341695.90195036-1.99791312 2.0085302-1.99791312h7.9829396c1.1092806 0 2.0085302.89826062 2.0085302 1.99791312v2.00208688h1.0049107c1.1018574 0 1.9950893.88743329 1.9950893 1.99961498v6.00077002c0 1.1043569-.8926228 1.999615-1.9950893 1.999615zm-1-3h-10v5.0018986c0 .5546075.44702548.9981014 1.0085302.9981014h7.9829396c.5565964 0 1.0085302-.4491701 1.0085302-.9981014zm-9 1h8v1h-8zm0 2h5v1h-5zm9-5c-.5522847 0-1-.44771525-1-1s.4477153-1 1-1 1 .44771525 1 1-.4477153 1-1 1z" fill-rule="evenodd"/></symbol><symbol id="icon-search" viewBox="0 0 22 22"><path d="M21.697 20.261a1.028 1.028 0 01.01 1.448 1.034 1.034 0 01-1.448-.01l-4.267-4.267A9.812 9.811 0 010 9.812a9.812 9.811 0 1117.43 6.182zM9.812 18.222A8.41 8.41 0 109.81 1.403a8.41 8.41 0 000 16.82z" fill-rule="evenodd"/></symbol><symbol id="icon-social-facebook" viewBox="0 0 24 24"><path d="m6.00368507 20c-1.10660471 0-2.00368507-.8945138-2.00368507-1.9940603v-12.01187942c0-1.10128908.89451376-1.99406028 1.99406028-1.99406028h12.01187942c1.1012891 0 1.9940603.89451376 1.9940603 1.99406028v12.01187942c0 1.1012891-.88679 1.9940603-2.0032184 1.9940603h-2.9570132v-6.1960818h2.0797387l.3114113-2.414723h-2.39115v-1.54164807c0-.69911803.1941355-1.1755439 1.1966615-1.1755439l1.2786739-.00055875v-2.15974763l-.2339477-.02492088c-.3441234-.03134957-.9500153-.07025255-1.6293054-.07025255-1.8435726 0-3.1057323 1.12531866-3.1057323 3.19187953v1.78079225h-2.0850778v2.414723h2.0850778v6.1960818z" fill-rule="evenodd"/></symbol><symbol id="icon-social-twitter" viewBox="0 0 24 24"><path d="m18.8767135 6.87445248c.7638174-.46908424 1.351611-1.21167363 1.6250764-2.09636345-.7135248.43394112-1.50406.74870123-2.3464594.91677702-.6695189-.73342162-1.6297913-1.19486605-2.6922204-1.19486605-2.0399895 0-3.6933555 1.69603749-3.6933555 3.78628909 0 .29642457.0314329.58673729.0942985.8617704-3.06469922-.15890802-5.78835241-1.66547825-7.60988389-3.9574208-.3174714.56076194-.49978171 1.21167363-.49978171 1.90536824 0 1.31404706.65223085 2.47224203 1.64236444 3.15218497-.60350999-.0198635-1.17401554-.1925232-1.67222562-.47366811v.04583885c0 1.83355406 1.27302891 3.36609966 2.96411421 3.71294696-.31118484.0886217-.63651445.1329326-.97441718.1329326-.2357461 0-.47149219-.0229194-.69466516-.0672303.47149219 1.5065703 1.83253297 2.6036468 3.44975116 2.632678-1.2651707 1.0160946-2.85724264 1.6196394-4.5891906 1.6196394-.29861172 0-.59093688-.0152796-.88011875-.0504227 1.63450624 1.0726291 3.57548241 1.6990934 5.66104951 1.6990934 6.79263079 0 10.50641749-5.7711113 10.50641749-10.7751859l-.0094298-.48894775c.7229547-.53478659 1.3516109-1.20250585 1.8419628-1.96190282-.6632323.30100846-1.3751855.50422736-2.1217148.59590507z" fill-rule="evenodd"/></symbol><symbol id="icon-social-youtube" viewBox="0 0 24 24"><path d="m10.1415 14.3973208-.0005625-5.19318431 4.863375 2.60554491zm9.963-7.92753362c-.6845625-.73643756-1.4518125-.73990314-1.803375-.7826454-2.518875-.18714178-6.2971875-.18714178-6.2971875-.18714178-.007875 0-3.7861875 0-6.3050625.18714178-.352125.04274226-1.1188125.04620784-1.8039375.7826454-.5394375.56084773-.7149375 1.8344515-.7149375 1.8344515s-.18 1.49597903-.18 2.99138042v1.4024082c0 1.495979.18 2.9913804.18 2.9913804s.1755 1.2736038.7149375 1.8344515c.685125.7364376 1.5845625.7133337 1.9850625.7901542 1.44.1420891 6.12.1859866 6.12.1859866s3.78225-.005776 6.301125-.1929178c.3515625-.0433198 1.1188125-.0467854 1.803375-.783223.5394375-.5608477.7155-1.8344515.7155-1.8344515s.18-1.4954014.18-2.9913804v-1.4024082c0-1.49540139-.18-2.99138042-.18-2.99138042s-.1760625-1.27360377-.7155-1.8344515z" fill-rule="evenodd"/></symbol><symbol id="icon-subject-medicine" viewBox="0 0 18 18"><path d="m12.5 8h-6.5c-1.65685425 0-3 1.34314575-3 3v1c0 1.6568542 1.34314575 3 3 3h1v-2h-.5c-.82842712 0-1.5-.6715729-1.5-1.5s.67157288-1.5 1.5-1.5h1.5 2 1 2c1.6568542 0 3-1.34314575 3-3v-1c0-1.65685425-1.3431458-3-3-3h-2v2h1.5c.8284271 0 1.5.67157288 1.5 1.5s-.6715729 1.5-1.5 1.5zm-5.5-1v-1h-3.5c-1.38071187 0-2.5-1.11928813-2.5-2.5s1.11928813-2.5 2.5-2.5h1.02786405c.46573528 0 .92507448.10843528 1.34164078.31671843l1.13382424.56691212c.06026365-1.05041141.93116291-1.88363055 1.99667093-1.88363055 1.1045695 0 2 .8954305 2 2h2c2.209139 0 4 1.790861 4 4v1c0 2.209139-1.790861 4-4 4h-2v1h2c1.1045695 0 2 .8954305 2 2s-.8954305 2-2 2h-2c0 1.1045695-.8954305 2-2 2s-2-.8954305-2-2h-1c-2.209139 0-4-1.790861-4-4v-1c0-2.209139 1.790861-4 4-4zm0-2v-2.05652691c-.14564246-.03538148-.28733393-.08714006-.42229124-.15461871l-1.15541752-.57770876c-.27771087-.13885544-.583937-.21114562-.89442719-.21114562h-1.02786405c-.82842712 0-1.5.67157288-1.5 1.5s.67157288 1.5 1.5 1.5zm4 1v1h1.5c.2761424 0 .5-.22385763.5-.5s-.2238576-.5-.5-.5zm-1 1v-5c0-.55228475-.44771525-1-1-1s-1 .44771525-1 1v5zm-2 4v5c0 .5522847.44771525 1 1 1s1-.4477153 1-1v-5zm3 2v2h2c.5522847 0 1-.4477153 1-1s-.4477153-1-1-1zm-4-1v-1h-.5c-.27614237 0-.5.2238576-.5.5s.22385763.5.5.5zm-3.5-9h1c.27614237 0 .5.22385763.5.5s-.22385763.5-.5.5h-1c-.27614237 0-.5-.22385763-.5-.5s.22385763-.5.5-.5z" fill-rule="evenodd"/></symbol><symbol id="icon-success" viewBox="0 0 18 18"><path d="m9 0c4.9705627 0 9 4.02943725 9 9 0 4.9705627-4.0294373 9-9 9-4.97056275 0-9-4.0294373-9-9 0-4.97056275 4.02943725-9 9-9zm3.4860198 4.98163161-4.71802968 5.50657859-2.62834168-2.02300024c-.42862421-.36730544-1.06564993-.30775346-1.42283677.13301307-.35718685.44076653-.29927542 1.0958383.12934879 1.46314377l3.40735508 2.7323063c.42215801.3385221 1.03700951.2798252 1.38749189-.1324571l5.38450527-6.33394549c.3613513-.43716226.3096573-1.09278382-.115462-1.46437175-.4251192-.37158792-1.0626796-.31842941-1.4240309.11873285z" fill-rule="evenodd"/></symbol><symbol id="icon-table" viewBox="0 0 18 18"><path d="m16.0049107 2c1.1018574 0 1.9950893.89706013 1.9950893 2.00585866v9.98828264c0 1.1078052-.8926228 2.0058587-1.9950893 2.0058587l-4.0059107-.001.001.001h-1l-.001-.001h-5l.001.001h-1l-.001-.001-3.00391071.001c-1.10185739 0-1.99508929-.8970601-1.99508929-2.0058587v-9.98828264c0-1.10780515.8926228-2.00585866 1.99508929-2.00585866zm-11.0059107 5h-3.999v6.9941413c0 .5572961.44630695 1.0058587.99508929 1.0058587h3.00391071zm6 0h-5v8h5zm5.0059107-4h-4.0059107v3h5.001v1h-5.001v7.999l4.0059107.001c.5487152 0 .9950893-.4488783.9950893-1.0058587v-9.98828264c0-.55729607-.446307-1.00585866-.9950893-1.00585866zm-12.5049107 9c.27614237 0 .5.2238576.5.5s-.22385763.5-.5.5h-1c-.27614237 0-.5-.2238576-.5-.5s.22385763-.5.5-.5zm12 0c.2761424 0 .5.2238576.5.5s-.2238576.5-.5.5h-2c-.2761424 0-.5-.2238576-.5-.5s.2238576-.5.5-.5zm-6 0c.27614237 0 .5.2238576.5.5s-.22385763.5-.5.5h-2c-.27614237 0-.5-.2238576-.5-.5s.22385763-.5.5-.5zm-6-2c.27614237 0 .5.2238576.5.5s-.22385763.5-.5.5h-1c-.27614237 0-.5-.2238576-.5-.5s.22385763-.5.5-.5zm12 0c.2761424 0 .5.2238576.5.5s-.2238576.5-.5.5h-2c-.2761424 0-.5-.2238576-.5-.5s.2238576-.5.5-.5zm-6 0c.27614237 0 .5.2238576.5.5s-.22385763.5-.5.5h-2c-.27614237 0-.5-.2238576-.5-.5s.22385763-.5.5-.5zm-6-2c.27614237 0 .5.22385763.5.5s-.22385763.5-.5.5h-1c-.27614237 0-.5-.22385763-.5-.5s.22385763-.5.5-.5zm12 0c.2761424 0 .5.22385763.5.5s-.2238576.5-.5.5h-2c-.2761424 0-.5-.22385763-.5-.5s.2238576-.5.5-.5zm-6 0c.27614237 0 .5.22385763.5.5s-.22385763.5-.5.5h-2c-.27614237 0-.5-.22385763-.5-.5s.22385763-.5.5-.5zm1.499-5h-5v3h5zm-6 0h-3.00391071c-.54871518 0-.99508929.44887827-.99508929 1.00585866v1.99414134h3.999z" fill-rule="evenodd"/></symbol><symbol id="icon-tick-circle" viewBox="0 0 24 24"><path d="m12 2c5.5228475 0 10 4.4771525 10 10s-4.4771525 10-10 10-10-4.4771525-10-10 4.4771525-10 10-10zm0 1c-4.97056275 0-9 4.02943725-9 9 0 4.9705627 4.02943725 9 9 9 4.9705627 0 9-4.0294373 9-9 0-4.97056275-4.0294373-9-9-9zm4.2199868 5.36606669c.3613514-.43716226.9989118-.49032077 1.424031-.11873285s.4768133 1.02720949.115462 1.46437175l-6.093335 6.94397871c-.3622945.4128716-.9897871.4562317-1.4054264.0971157l-3.89719065-3.3672071c-.42862421-.3673054-.48653564-1.0223772-.1293488-1.4631437s.99421256-.5003185 1.42283677-.1330131l3.11097438 2.6987741z" fill-rule="evenodd"/></symbol><symbol id="icon-tick" viewBox="0 0 16 16"><path d="m6.76799012 9.21106946-3.1109744-2.58349728c-.42862421-.35161617-1.06564993-.29460792-1.42283677.12733148s-.29927541 1.04903009.1293488 1.40064626l3.91576307 3.23873978c.41034319.3393961 1.01467563.2976897 1.37450571-.0948578l6.10568327-6.660841c.3613513-.41848908.3096572-1.04610608-.115462-1.4018218-.4251192-.35571573-1.0626796-.30482786-1.424031.11366122z" fill-rule="evenodd"/></symbol><symbol id="icon-update" viewBox="0 0 18 18"><path d="m1 13v1c0 .5522847.44771525 1 1 1h14c.5522847 0 1-.4477153 1-1v-1h-1v-10h-14v10zm16-1h1v2c0 1.1045695-.8954305 2-2 2h-14c-1.1045695 0-2-.8954305-2-2v-2h1v-9c0-.55228475.44771525-1 1-1h14c.5522847 0 1 .44771525 1 1zm-1 0v1h-4.5857864l-1 1h-2.82842716l-1-1h-4.58578644v-1h5l1 1h2l1-1zm-13-8h12v7h-12zm1 1v5h10v-5zm1 1h4v1h-4zm0 2h4v1h-4z" fill-rule="evenodd"/></symbol><symbol id="icon-upload" viewBox="0 0 18 18"><path d="m10.0046024 0c.5497429 0 1.3179837.32258606 1.707238.71184039l4.5763192 4.57631922c.3931386.39313859.7118404 1.16760135.7118404 1.71431368v8.98899651c0 1.1092806-.8945138 2.0085302-1.9940603 2.0085302h-12.01187942c-1.10128908 0-1.99406028-.8926228-1.99406028-1.9950893v-14.00982141c0-1.10185739.88743329-1.99508929 1.99961498-1.99508929zm0 1h-7.00498742c-.55709576 0-.99961498.44271433-.99961498.99508929v14.00982141c0 .5500396.44491393.9950893.99406028.9950893h12.01187942c.5463747 0 .9940603-.4506622.9940603-1.0085302v-8.98899651c0-.28393444-.2150684-.80332809-.4189472-1.0072069l-4.5763192-4.57631922c-.2038461-.20384606-.718603-.41894717-1.0001312-.41894717zm-1.85576936 4.14572769c.19483374-.19483375.51177826-.19377714.70556874.00001334l2.59099082 2.59099079c.1948411.19484112.1904373.51514474.0027906.70279143-.1932998.19329987-.5046517.19237083-.7001856-.00692852l-1.74638687-1.7800176v6.14827687c0 .2717771-.23193359.492096-.5.492096-.27614237 0-.5-.216372-.5-.492096v-6.14827641l-1.74627892 1.77990922c-.1933927.1971171-.51252214.19455839-.70016883.0069117-.19329987-.19329988-.19100584-.50899493.00277731-.70277808z" fill-rule="evenodd"/></symbol><symbol id="icon-video" viewBox="0 0 18 18"><path d="m16.0049107 2c1.1018574 0 1.9950893.89706013 1.9950893 2.00585866v9.98828264c0 1.1078052-.8926228 2.0058587-1.9950893 2.0058587h-14.00982141c-1.10185739 0-1.99508929-.8970601-1.99508929-2.0058587v-9.98828264c0-1.10780515.8926228-2.00585866 1.99508929-2.00585866zm0 1h-14.00982141c-.54871518 0-.99508929.44887827-.99508929 1.00585866v9.98828264c0 .5572961.44630695 1.0058587.99508929 1.0058587h14.00982141c.5487152 0 .9950893-.4488783.9950893-1.0058587v-9.98828264c0-.55729607-.446307-1.00585866-.9950893-1.00585866zm-8.30912922 2.24944486 4.60460462 2.73982242c.9365543.55726659.9290753 1.46522435 0 2.01804082l-4.60460462 2.7398224c-.93655425.5572666-1.69578148.1645632-1.69578148-.8937585v-5.71016863c0-1.05087579.76670616-1.446575 1.69578148-.89375851zm-.67492769.96085624v5.5750128c0 .2995102-.10753745.2442517.16578928.0847713l4.58452283-2.67497259c.3050619-.17799716.3051624-.21655446 0-.39461026l-4.58452283-2.67497264c-.26630747-.15538481-.16578928-.20699944-.16578928.08477139z" fill-rule="evenodd"/></symbol><symbol id="icon-warning" viewBox="0 0 18 18"><path d="m9 11.75c.69035594 0 1.25.5596441 1.25 1.25s-.55964406 1.25-1.25 1.25-1.25-.5596441-1.25-1.25.55964406-1.25 1.25-1.25zm.41320045-7.75c.55228475 0 1.00000005.44771525 1.00000005 1l-.0034543.08304548-.3333333 4c-.043191.51829212-.47645714.91695452-.99654578.91695452h-.15973424c-.52008864 0-.95335475-.3986624-.99654576-.91695452l-.33333333-4c-.04586475-.55037702.36312325-1.03372649.91350028-1.07959124l.04148683-.00259031zm-.41320045 14c-4.97056275 0-9-4.0294373-9-9 0-4.97056275 4.02943725-9 9-9 4.9705627 0 9 4.02943725 9 9 0 4.9705627-4.0294373 9-9 9z" fill-rule="evenodd"/></symbol><symbol id="icon-checklist-banner" viewBox="0 0 56.69 56.69"><path style="fill:none" d="M0 0h56.69v56.69H0z"/><clipPath id="b"><use xlink:href="#a" style="overflow:visible"/></clipPath><path d="M21.14 34.46c0-6.77 5.48-12.26 12.24-12.26s12.24 5.49 12.24 12.26-5.48 12.26-12.24 12.26c-6.76-.01-12.24-5.49-12.24-12.26zm19.33 10.66 10.23 9.22s1.21 1.09 2.3-.12l2.09-2.32s1.09-1.21-.12-2.3l-10.23-9.22m-19.29-5.92c0-4.38 3.55-7.94 7.93-7.94s7.93 3.55 7.93 7.94c0 4.38-3.55 7.94-7.93 7.94-4.38-.01-7.93-3.56-7.93-7.94zm17.58 12.99 4.14-4.81" style="clip-path:url(#b);fill:none;stroke:#01324b;stroke-width:2;stroke-linecap:round"/><path d="M8.26 9.75H28.6M8.26 15.98H28.6m-20.34 6.2h12.5m14.42-5.2V4.86s0-2.93-2.93-2.93H4.13s-2.93 0-2.93 2.93v37.57s0 2.93 2.93 2.93h15.01M8.26 9.75H28.6M8.26 15.98H28.6m-20.34 6.2h12.5" style="clip-path:url(#b);fill:none;stroke:#01324b;stroke-width:2;stroke-linecap:round;stroke-linejoin:round"/></symbol><symbol id="icon-chevron-down" viewBox="0 0 16 16"><path d="m5.58578644 3-3.29289322-3.29289322c-.39052429-.39052429-.39052429-1.02368927 0-1.41421356s1.02368927-.39052429 1.41421356 0l4 4c.39052429.39052429.39052429 1.02368927 0 1.41421356l-4 4c-.39052429.39052429-1.02368927.39052429-1.41421356 0s-.39052429-1.02368927 0-1.41421356z" fill-rule="evenodd" transform="matrix(0 1 -1 0 11 1)"/></symbol><symbol id="icon-eds-i-arrow-right-medium" viewBox="0 0 24 24"><path d="m12.728 3.293 7.98 7.99a.996.996 0 0 1 .281.561l.011.157c0 .32-.15.605-.384.788l-7.908 7.918a1 1 0 0 1-1.416-1.414L17.576 13H4a1 1 0 0 1 0-2h13.598l-6.285-6.293a1 1 0 0 1-.082-1.32l.083-.095a1 1 0 0 1 1.414.001Z"/></symbol><symbol id="icon-eds-i-chevron-down-medium" viewBox="0 0 16 16"><path d="m2.00087166 7h4.99912834v-4.99912834c0-.55276616.44386482-1.00087166 1-1.00087166.55228475 0 1 .44463086 1 1.00087166v4.99912834h4.9991283c.5527662 0 1.0008717.44386482 1.0008717 1 0 .55228475-.4446309 1-1.0008717 1h-4.9991283v4.9991283c0 .5527662-.44386482 1.0008717-1 1.0008717-.55228475 0-1-.4446309-1-1.0008717v-4.9991283h-4.99912834c-.55276616 0-1.00087166-.44386482-1.00087166-1 0-.55228475.44463086-1 1.00087166-1z" fill-rule="evenodd"/></symbol><symbol id="icon-eds-i-chevron-down-small" viewBox="0 0 16 16"><path d="M13.692 5.278a1 1 0 0 1 .03 1.414L9.103 11.51a1.491 1.491 0 0 1-2.188.019L2.278 6.692a1 1 0 0 1 1.444-1.384L8 9.771l4.278-4.463a1 1 0 0 1 1.318-.111l.096.081Z"/></symbol><symbol id="icon-eds-i-chevron-right-medium" viewBox="0 0 10 10"><path d="m5.96738168 4.70639573 2.39518594-2.41447274c.37913917-.38219212.98637524-.38972225 1.35419292-.01894278.37750606.38054586.37784436.99719163-.00013556 1.37821513l-4.03074001 4.06319683c-.37758093.38062133-.98937525.38100976-1.367372-.00003075l-4.03091981-4.06337806c-.37759778-.38063832-.38381821-.99150444-.01600053-1.3622839.37750607-.38054587.98772445-.38240057 1.37006824.00302197l2.39538588 2.4146743.96295325.98624457z" fill-rule="evenodd" transform="matrix(0 -1 1 0 0 10)"/></symbol><symbol id="icon-eds-i-chevron-right-small" viewBox="0 0 10 10"><path d="m5.96738168 4.70639573 2.39518594-2.41447274c.37913917-.38219212.98637524-.38972225 1.35419292-.01894278.37750606.38054586.37784436.99719163-.00013556 1.37821513l-4.03074001 4.06319683c-.37758093.38062133-.98937525.38100976-1.367372-.00003075l-4.03091981-4.06337806c-.37759778-.38063832-.38381821-.99150444-.01600053-1.3622839.37750607-.38054587.98772445-.38240057 1.37006824.00302197l2.39538588 2.4146743.96295325.98624457z" fill-rule="evenodd" transform="matrix(0 -1 1 0 0 10)"/></symbol><symbol id="icon-eds-i-chevron-up-medium" viewBox="0 0 16 16"><path d="m2.00087166 7h11.99825664c.5527662 0 1.0008717.44386482 1.0008717 1 0 .55228475-.4446309 1-1.0008717 1h-11.99825664c-.55276616 0-1.00087166-.44386482-1.00087166-1 0-.55228475.44463086-1 1.00087166-1z" fill-rule="evenodd"/></symbol><symbol id="icon-eds-i-close-medium" viewBox="0 0 16 16"><path d="m2.29679575 12.2772478c-.39658757.3965876-.39438847 1.0328109-.00062148 1.4265779.39651227.3965123 1.03246768.3934888 1.42657791-.0006214l4.27724782-4.27724787 4.2772478 4.27724787c.3965876.3965875 1.0328109.3943884 1.4265779.0006214.3965123-.3965122.3934888-1.0324677-.0006214-1.4265779l-4.27724787-4.2772478 4.27724787-4.27724782c.3965875-.39658757.3943884-1.03281091.0006214-1.42657791-.3965122-.39651226-1.0324677-.39348875-1.4265779.00062148l-4.2772478 4.27724782-4.27724782-4.27724782c-.39658757-.39658757-1.03281091-.39438847-1.42657791-.00062148-.39651226.39651227-.39348875 1.03246768.00062148 1.42657791l4.27724782 4.27724782z" fill-rule="evenodd"/></symbol><symbol id="icon-eds-i-download-medium" viewBox="0 0 16 16"><path d="m12.9975267 12.999368c.5467123 0 1.0024733.4478567 1.0024733 1.000316 0 .5563109-.4488226 1.000316-1.0024733 1.000316h-9.99505341c-.54671233 0-1.00247329-.4478567-1.00247329-1.000316 0-.5563109.44882258-1.000316 1.00247329-1.000316zm-4.9975267-11.999368c.55228475 0 1 .44497754 1 .99589209v6.80214418l2.4816273-2.48241149c.3928222-.39294628 1.0219732-.4006883 1.4030652-.01947579.3911302.39125371.3914806 1.02525073-.0001404 1.41699553l-4.17620792 4.17752758c-.39120769.3913313-1.02508144.3917306-1.41671995-.0000316l-4.17639421-4.17771394c-.39122513-.39134876-.39767006-1.01940351-.01657797-1.40061601.39113012-.39125372 1.02337105-.3931606 1.41951349.00310701l2.48183446 2.48261871v-6.80214418c0-.55001601.44386482-.99589209 1-.99589209z" fill-rule="evenodd"/></symbol><symbol id="icon-eds-i-info-filled-medium" viewBox="0 0 18 18"><path d="m9 0c4.9705627 0 9 4.02943725 9 9 0 4.9705627-4.0294373 9-9 9-4.97056275 0-9-4.0294373-9-9 0-4.97056275 4.02943725-9 9-9zm0 7h-1.5l-.11662113.00672773c-.49733868.05776511-.88337887.48043643-.88337887.99327227 0 .47338693.32893365.86994729.77070917.97358929l.1126697.01968298.11662113.00672773h.5v3h-.5l-.11662113.0067277c-.42082504.0488782-.76196299.3590206-.85696816.7639815l-.01968298.1126697-.00672773.1166211.00672773.1166211c.04887817.4208251.35902055.761963.76398144.8569682l.1126697.019683.11662113.0067277h3l.1166211-.0067277c.4973387-.0577651.8833789-.4804365.8833789-.9932723 0-.4733869-.3289337-.8699473-.7707092-.9735893l-.1126697-.019683-.1166211-.0067277h-.5v-4l-.00672773-.11662113c-.04887817-.42082504-.35902055-.76196299-.76398144-.85696816l-.1126697-.01968298zm0-3.25c-.69035594 0-1.25.55964406-1.25 1.25s.55964406 1.25 1.25 1.25 1.25-.55964406 1.25-1.25-.55964406-1.25-1.25-1.25z" fill-rule="evenodd"/></symbol><symbol id="icon-eds-i-mail-medium" viewBox="0 0 24 24"><path d="m19.462 0c1.413 0 2.538 1.184 2.538 2.619v12.762c0 1.435-1.125 2.619-2.538 2.619h-16.924c-1.413 0-2.538-1.184-2.538-2.619v-12.762c0-1.435 1.125-2.619 2.538-2.619zm.538 5.158-7.378 6.258a2.549 2.549 0 0 1 -3.253-.008l-7.369-6.248v10.222c0 .353.253.619.538.619h16.924c.285 0 .538-.266.538-.619zm-.538-3.158h-16.924c-.264 0-.5.228-.534.542l8.65 7.334c.2.165.492.165.684.007l8.656-7.342-.001-.025c-.044-.3-.274-.516-.531-.516z"/></symbol><symbol id="icon-eds-i-menu-medium" viewBox="0 0 24 24"><path d="M21 4a1 1 0 0 1 0 2H3a1 1 0 1 1 0-2h18Zm-4 7a1 1 0 0 1 0 2H3a1 1 0 0 1 0-2h14Zm4 7a1 1 0 0 1 0 2H3a1 1 0 0 1 0-2h18Z"/></symbol><symbol id="icon-eds-i-search-medium" viewBox="0 0 24 24"><path d="M11 1c5.523 0 10 4.477 10 10 0 2.4-.846 4.604-2.256 6.328l3.963 3.965a1 1 0 0 1-1.414 1.414l-3.965-3.963A9.959 9.959 0 0 1 11 21C5.477 21 1 16.523 1 11S5.477 1 11 1Zm0 2a8 8 0 1 0 0 16 8 8 0 0 0 0-16Z"/></symbol><symbol id="icon-eds-i-user-single-medium" viewBox="0 0 24 24"><path d="M12 1a5 5 0 1 1 0 10 5 5 0 0 1 0-10Zm0 2a3 3 0 1 0 0 6 3 3 0 0 0 0-6Zm-.406 9.008a8.965 8.965 0 0 1 6.596 2.494A9.161 9.161 0 0 1 21 21.025V22a1 1 0 0 1-1 1H4a1 1 0 0 1-1-1v-.985c.05-4.825 3.815-8.777 8.594-9.007Zm.39 1.992-.299.006c-3.63.175-6.518 3.127-6.678 6.775L5 21h13.998l-.009-.268a7.157 7.157 0 0 0-1.97-4.573l-.214-.213A6.967 6.967 0 0 0 11.984 14Z"/></symbol><symbol id="icon-eds-i-warning-filled-medium" viewBox="0 0 18 18"><path d="m9 11.75c.69035594 0 1.25.5596441 1.25 1.25s-.55964406 1.25-1.25 1.25-1.25-.5596441-1.25-1.25.55964406-1.25 1.25-1.25zm.41320045-7.75c.55228475 0 1.00000005.44771525 1.00000005 1l-.0034543.08304548-.3333333 4c-.043191.51829212-.47645714.91695452-.99654578.91695452h-.15973424c-.52008864 0-.95335475-.3986624-.99654576-.91695452l-.33333333-4c-.04586475-.55037702.36312325-1.03372649.91350028-1.07959124l.04148683-.00259031zm-.41320045 14c-4.97056275 0-9-4.0294373-9-9 0-4.97056275 4.02943725-9 9-9 4.9705627 0 9 4.02943725 9 9 0 4.9705627-4.0294373 9-9 9z" fill-rule="evenodd"/></symbol><symbol id="icon-expand-image" viewBox="0 0 18 18"><path d="m7.49754099 11.9178212c.38955542-.3895554.38761957-1.0207846-.00290473-1.4113089-.39324695-.3932469-1.02238878-.3918247-1.41130883-.0029047l-4.10273549 4.1027355.00055454-3.5103985c.00008852-.5603185-.44832171-1.006032-1.00155062-1.0059446-.53903074.0000852-.97857527.4487442-.97866268 1.0021075l-.00093318 5.9072465c-.00008751.553948.44841131 1.001882 1.00174994 1.0017946l5.906983-.0009331c.5539233-.0000875 1.00197907-.4486389 1.00206646-1.0018679.00008515-.5390307-.45026621-.9784332-1.00588841-.9783454l-3.51010549.0005545zm3.00571741-5.83449376c-.3895554.38955541-.3876196 1.02078454.0029047 1.41130883.393247.39324696 1.0223888.39182478 1.4113089.00290473l4.1027355-4.10273549-.0005546 3.5103985c-.0000885.56031852.4483217 1.006032 1.0015506 1.00594461.5390308-.00008516.9785753-.44874418.9786627-1.00210749l.0009332-5.9072465c.0000875-.553948-.4484113-1.00188204-1.0017499-1.00179463l-5.906983.00093313c-.5539233.00008751-1.0019791.44863892-1.0020665 1.00186784-.0000852.53903074.4502662.97843325 1.0058884.97834547l3.5101055-.00055449z" fill-rule="evenodd"/></symbol><symbol id="icon-github" viewBox="0 0 100 100"><path fill-rule="evenodd" clip-rule="evenodd" d="M48.854 0C21.839 0 0 22 0 49.217c0 21.756 13.993 40.172 33.405 46.69 2.427.49 3.316-1.059 3.316-2.362 0-1.141-.08-5.052-.08-9.127-13.59 2.934-16.42-5.867-16.42-5.867-2.184-5.704-5.42-7.17-5.42-7.17-4.448-3.015.324-3.015.324-3.015 4.934.326 7.523 5.052 7.523 5.052 4.367 7.496 11.404 5.378 14.235 4.074.404-3.178 1.699-5.378 3.074-6.6-10.839-1.141-22.243-5.378-22.243-24.283 0-5.378 1.94-9.778 5.014-13.2-.485-1.222-2.184-6.275.486-13.038 0 0 4.125-1.304 13.426 5.052a46.97 46.97 0 0 1 12.214-1.63c4.125 0 8.33.571 12.213 1.63 9.302-6.356 13.427-5.052 13.427-5.052 2.67 6.763.97 11.816.485 13.038 3.155 3.422 5.015 7.822 5.015 13.2 0 18.905-11.404 23.06-22.324 24.283 1.78 1.548 3.316 4.481 3.316 9.126 0 6.6-.08 11.897-.08 13.526 0 1.304.89 2.853 3.316 2.364 19.412-6.52 33.405-24.935 33.405-46.691C97.707 22 75.788 0 48.854 0z"/></symbol><symbol id="icon-springer-arrow-left"><path d="M15 7a1 1 0 000-2H3.385l2.482-2.482a.994.994 0 00.02-1.403 1.001 1.001 0 00-1.417 0L.294 5.292a1.001 1.001 0 000 1.416l4.176 4.177a.991.991 0 001.4.016 1 1 0 00-.003-1.42L3.385 7H15z"/></symbol><symbol id="icon-springer-arrow-right"><path d="M1 7a1 1 0 010-2h11.615l-2.482-2.482a.994.994 0 01-.02-1.403 1.001 1.001 0 011.417 0l4.176 4.177a1.001 1.001 0 010 1.416l-4.176 4.177a.991.991 0 01-1.4.016 1 1 0 01.003-1.42L12.615 7H1z"/></symbol><symbol id="icon-submit-open" viewBox="0 0 16 17"><path d="M12 0c1.10457 0 2 .895431 2 2v5c0 .276142-.223858.5-.5.5S13 7.276142 13 7V2c0-.512836-.38604-.935507-.883379-.993272L12 1H6v3c0 1.10457-.89543 2-2 2H1v8c0 .512836.38604.935507.883379.993272L2 15h6.5c.276142 0 .5.223858.5.5s-.223858.5-.5.5H2c-1.104569 0-2-.89543-2-2V5.828427c0-.530433.210714-1.039141.585786-1.414213L4.414214.585786C4.789286.210714 5.297994 0 5.828427 0H12Zm3.41 11.14c.250899.250899.250274.659726 0 .91-.242954.242954-.649606.245216-.9-.01l-1.863671-1.900337.001043 5.869492c0 .356992-.289839.637138-.647372.637138-.347077 0-.647371-.285256-.647371-.637138l-.001043-5.869492L9.5 12.04c-.253166.258042-.649726.260274-.9.01-.242954-.242954-.252269-.657731 0-.91l2.942184-2.951303c.250908-.250909.66127-.252277.91353-.000017L15.41 11.14ZM5 1.413 1.413 5H4c.552285 0 1-.447715 1-1V1.413ZM11 3c.276142 0 .5.223858.5.5s-.223858.5-.5.5H7.5c-.276142 0-.5-.223858-.5-.5s.223858-.5.5-.5H11Zm0 2c.276142 0 .5.223858.5.5s-.223858.5-.5.5H7.5c-.276142 0-.5-.223858-.5-.5s.223858-.5.5-.5H11Z" fill-rule="nonzero"/></symbol></svg> </div> </footer> <div class="c-site-messages message u-hide u-hide-print c-site-messages--nature-briefing c-site-messages--nature-briefing-email-variant c-site-messages--nature-briefing-redesign-2020 sans-serif " data-component-id="nature-briefing-banner" data-component-expirydays="30" data-component-trigger-scroll-percentage="15" data-track="in-view" data-track-action="in-view" data-track-category="nature briefing" data-track-label="Briefing banner visible: Flagship"> <div class="c-site-messages__banner-large"> <div class="c-site-messages__close-container"> <button class="c-site-messages__close" data-track="click" data-track-category="nature briefing" data-track-label="Briefing banner dismiss: Flagship"> <svg width="25px" height="25px" focusable="false" aria-hidden="true" viewBox="0 0 25 25" version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <title>Close banner</title> <defs></defs> <g stroke="none" stroke-width="1" fill="none" fill-rule="evenodd"> <rect opacity="0" x="0" y="0" width="25" height="25"></rect> <path d="M6.29679575,16.2772478 C5.90020818,16.6738354 5.90240728,17.3100587 6.29617427,17.7038257 C6.69268654,18.100338 7.32864195,18.0973145 7.72275218,17.7032043 L12,13.4259564 L16.2772478,17.7032043 C16.6738354,18.0997918 17.3100587,18.0975927 17.7038257,17.7038257 C18.100338,17.3073135 18.0973145,16.671358 17.7032043,16.2772478 L13.4259564,12 L17.7032043,7.72275218 C18.0997918,7.32616461 18.0975927,6.68994127 17.7038257,6.29617427 C17.3073135,5.89966201 16.671358,5.90268552 16.2772478,6.29679575 L12,10.5740436 L7.72275218,6.29679575 C7.32616461,5.90020818 6.68994127,5.90240728 6.29617427,6.29617427 C5.89966201,6.69268654 5.90268552,7.32864195 6.29679575,7.72275218 L10.5740436,12 L6.29679575,16.2772478 Z" fill="#ffffff"></path> </g> </svg> <span class="visually-hidden">Close</span> </button> </div> <div class="c-site-messages__form-container"> <div class="grid grid-12 last"> <div class="grid grid-4"> <img alt="Nature Briefing AI and Robotics" src="/static/images/logos/nature-briefing-ai-and-robotics-logo-51b3cf6c52.svg" width="400" height="40"> <p class="c-site-messages--nature-briefing__strapline extra-tight-line-height">Sign up for the <em>Nature Briefing: AI and Robotics</em> newsletter — what matters in AI and robotics research, free to your inbox weekly.</p> </div> <div class="grid grid-8 last"> <form action="https://www.nature.com/briefing/ai_and_robotics" method="post" data-location="banner" data-track="signup_nature_briefing_banner" data-track-action="transmit-form" data-track-category="nature briefing" data-track-label="Briefing banner submit: Flagship"> <input id="briefing-banner-signup-form-input-track-originReferralPoint" type="hidden" name="track_originReferralPoint" value="AIAndRoboticsBriefingBanner"> <input id="briefing-banner-signup-form-input-track-formType" type="hidden" name="track_formType" value="DirectEmailBanner"> <input type="hidden" value="false" name="gdpr_tick" id="gdpr_tick_banner"> <input type="hidden" value="false" name="marketing" id="marketing_input_banner"> <input type="hidden" value="false" name="marketing_tick" id="marketing_tick_banner"> <input type="hidden" value="AIAndRoboticsBriefingBanner" name="brieferEntryPoint" id="brieferEntryPoint_banner"> <label class="nature-briefing-banner__email-label" for="emailAddress">Email address</label> <div class="nature-briefing-banner__email-wrapper"> <input class="nature-briefing-banner__email-input box-sizing text14" type="email" id="emailAddress" name="emailAddress" value="" placeholder="e.g. jo.smith@university.ac.uk" required data-test-element="briefing-emailbanner-email-input"> <input type="hidden" value="true" name="N:ai_and_robotics" id="defaultNewsletter_banner"> <button type="submit" class="nature-briefing-banner__submit-button box-sizing text14" data-test-element="briefing-emailbanner-signup-button">Sign up</button> </div> <div class="nature-briefing-banner__checkbox-wrapper grid grid-12 last"> <input class="nature-briefing-banner__checkbox-checkbox" id="gdpr-briefing-banner-checkbox" type="checkbox" name="gdpr" value="true" data-test-element="briefing-emailbanner-gdpr-checkbox" required> <label class="nature-briefing-banner__checkbox-label box-sizing text13 sans-serif block tighten-line-height" for="gdpr-briefing-banner-checkbox">I agree my information will be processed in accordance with the <em>Nature</em> and Springer Nature Limited <a href="https://www.nature.com/info/privacy">Privacy Policy</a>.</label> </div> </form> </div> </div> </div> </div> <div class="c-site-messages__banner-small"> <div class="c-site-messages__close-container"> <button class="c-site-messages__close" data-track="click" data-track-category="nature briefing" data-track-label="Briefing banner dismiss: Flagship"> <svg width="25px" height="25px" focusable="false" aria-hidden="true" viewBox="0 0 25 25" version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <title>Close banner</title> <defs></defs> <g stroke="none" stroke-width="1" fill="none" fill-rule="evenodd"> <rect opacity="0" x="0" y="0" width="25" height="25"></rect> <path d="M6.29679575,16.2772478 C5.90020818,16.6738354 5.90240728,17.3100587 6.29617427,17.7038257 C6.69268654,18.100338 7.32864195,18.0973145 7.72275218,17.7032043 L12,13.4259564 L16.2772478,17.7032043 C16.6738354,18.0997918 17.3100587,18.0975927 17.7038257,17.7038257 C18.100338,17.3073135 18.0973145,16.671358 17.7032043,16.2772478 L13.4259564,12 L17.7032043,7.72275218 C18.0997918,7.32616461 18.0975927,6.68994127 17.7038257,6.29617427 C17.3073135,5.89966201 16.671358,5.90268552 16.2772478,6.29679575 L12,10.5740436 L7.72275218,6.29679575 C7.32616461,5.90020818 6.68994127,5.90240728 6.29617427,6.29617427 C5.89966201,6.69268654 5.90268552,7.32864195 6.29679575,7.72275218 L10.5740436,12 L6.29679575,16.2772478 Z" fill="#ffffff"></path> </g> </svg> <span class="visually-hidden">Close</span> </button> </div> <div class="c-site-messages__content text14"> <span class="c-site-messages--nature-briefing__strapline strong">Get the most important science stories of the day, free in your inbox.</span> <a class="nature-briefing__link text14 sans-serif" data-track="click" data-track-category="nature briefing" data-track-label="Small-screen banner CTA to site" data-test-element="briefing-banner-link" target="_blank" rel="noreferrer noopener" href="/briefing/ai-and-robotics/?brieferEntryPoint=AIAndRoboticsBriefingBanner">Sign up for Nature Briefing: AI and Robotics </a> </div> </div> </div> <noscript> <img hidden src="https://verify.nature.com/verify/nature.png" width="0" height="0" style="display: none" alt=""> </noscript> <script src="//content.readcube.com/ping?doi=10.1038/s41586-024-08032-5&format=js&last_modified=2024-09-26" async></script> </body> </html>

CINXE.COM

Addendum: A graph placement methodology for fast chip design | Nature