A quadratic programming approach to simultaneous buffer insertion/sizing and wire sizing

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x-description="Expandable link section, show/hide based on state." class="" x-show="open" x-cloak> <ul class=""> <li class="dropdown-item sub-menu-list-item text-gray-800"> <a href="/about/media-bookdirectory/governing-documents" class="menu-item-link flex px-6 py-3 font-semibold text-gray-900 hover__text-gray-500 border-l-16 border-primary-200 ml-2 rounded-lg my-1 focus__text-gray-500 hover__bg-gray-50 no-underline link-underline">Constitution & Bylaws</a> </li> <li class="dropdown-item sub-menu-list-item text-gray-800"> <a href="/about/meeting-minutes-and-presentations" class="menu-item-link flex px-6 py-3 font-semibold text-gray-900 hover__text-gray-500 border-l-16 border-primary-200 ml-2 rounded-lg my-1 focus__text-gray-500 hover__bg-gray-50 no-underline link-underline">Minutes & Presentations</a> </li> </ul> </div> </div> </li> <li class="dropdown-item sub-menu-list-item text-gray-800 expanded nav-item nav-item expanded nav-item has-sub-menu nav-item"> <div x-data="{ open: false }" x-title="Slide-over menu - Publicity"> <button type="button" class="flex items-center justify-between w-full px-6 py-3 text-left text-gray-900 transition-colors duration-150 ease-in-out border-l-8 hover__text-gray-500 hover__bg-gray-100 focus__text-gray-500 focus__bg-gray-50 bg-gray-50 border-primary-400 ml-1 group focus__outline-none" x-state:on="Current" x-state:off="Default" @click="open = !open" aria-expanded="false" x-bind:aria-expanded="open.toString()" x-state-description=""> <span class="heading--nav--second-level menu-item-link inline-flex text-base mb-0 font-bold">Publicity</span> <div class="duration-150 ease-in-out transform" x-state:on="Expanded" x-state:off="Collapsed" :class="{ 'rotate-90': open, '': !(open) }"> <i class="fa-regular fa-chevron-right"></i> </div> </button> <div x-description="Expandable link section, show/hide based on state." class="" x-show="open" x-cloak> <ul class=""> <li class="dropdown-item sub-menu-list-item text-gray-800"> <a href="/about/publicity-resources-and-requests" class="menu-item-link flex px-6 py-3 font-semibold text-gray-900 hover__text-gray-500 border-l-16 border-primary-200 ml-2 rounded-lg my-1 focus__text-gray-500 hover__bg-gray-50 no-underline link-underline">Publicity Resources</a> </li> <li class="dropdown-item sub-menu-list-item text-gray-800"> <a href="https://www.youtube.com/channel/UCtV0i4UH8cElzn4lgl7VrAw?view_as=subscriber" class="menu-item-link flex px-6 py-3 font-semibold text-gray-900 hover__text-gray-500 border-l-16 border-primary-200 ml-2 rounded-lg my-1 focus__text-gray-500 hover__bg-gray-50 no-underline link-underline" rel="noreferrer">YouTube Presentations</a> </li> </ul> </div> </div> </li> <li class="dropdown-item sub-menu-list-item text-gray-800 expanded nav-item nav-item expanded nav-item has-sub-menu nav-item"> <div x-data="{ open: false }" x-title="Slide-over menu - Staff"> <button type="button" class="flex items-center justify-between w-full px-6 py-3 text-left text-gray-900 transition-colors duration-150 ease-in-out border-l-8 hover__text-gray-500 hover__bg-gray-100 focus__text-gray-500 focus__bg-gray-50 bg-gray-50 border-primary-400 ml-1 group focus__outline-none" x-state:on="Current" x-state:off="Default" @click="open = !open" aria-expanded="false" x-bind:aria-expanded="open.toString()" x-state-description=""> <span class="heading--nav--second-level menu-item-link inline-flex text-base mb-0 font-bold">Staff</span> <div class="duration-150 ease-in-out transform" x-state:on="Expanded" x-state:off="Collapsed" :class="{ 'rotate-90': open, '': !(open) }"> <i class="fa-regular fa-chevron-right"></i> </div> </button> <div x-description="Expandable link section, show/hide based on state." class="" x-show="open" x-cloak> <ul class=""> <li class="dropdown-item sub-menu-list-item text-gray-800"> <a href="/about/staff/operations-manager" class="menu-item-link flex px-6 py-3 font-semibold text-gray-900 hover__text-gray-500 border-l-16 border-primary-200 ml-2 rounded-lg my-1 focus__text-gray-500 hover__bg-gray-50 no-underline link-underline" data-drupal-link-system-path="node/2118">Operations Manager</a> </li> </ul> </div> </div> </li> </ul> </div> </div> </li> <li class="nav-item nav-item expanded nav-item nav-item expanded nav-item has-sub-menu nav-item"> <div x-data="{ open: false }" x-title="Slide-over menu - Awards"> <button type="button" class="flex items-center justify-between w-full px-6 py-3 text-left transition-colors duration-150 ease-in-out group focus__outline-none" x-state:on="Current" x-state:off="Default" @click="open = !open" aria-expanded="false" x-bind:aria-expanded="open.toString()" x-state-description="" :class="{ 'hover__text-gray-500 hover__bg-gray-50 focus__bg-gray-50' : !(open), 'hover__text-gray-50 bg-primary-600 text-white' : open }"> <span class="menu-item-link inline-flex no-underline font-bold">Awards</span> <div class="duration-150 ease-in-out transform" x-state:on="Expanded" x-state:off="Collapsed" :class="{ 'rotate-90': open, '': !(open) }"> <i class="fa-regular fa-chevron-right"></i> </div> </button> <div x-description="Expandable link section, show/hide based on state." class="" x-show="open" x-cloak> <ul class=""> <li class="dropdown-item sub-menu-list-item text-gray-800 expanded nav-item nav-item expanded nav-item has-sub-menu nav-item"> <div x-data="{ open: false }" x-title="Slide-over menu - Awards & Recognitions Program"> <button type="button" class="flex items-center justify-between w-full px-6 py-3 text-left text-gray-900 transition-colors duration-150 ease-in-out border-l-8 hover__text-gray-500 hover__bg-gray-100 focus__text-gray-500 focus__bg-gray-50 bg-gray-50 border-primary-400 ml-1 group focus__outline-none" x-state:on="Current" x-state:off="Default" @click="open = !open" aria-expanded="false" x-bind:aria-expanded="open.toString()" x-state-description=""> <span class="heading--nav--second-level menu-item-link inline-flex text-base mb-0 font-bold">Awards & Recognitions Program</span> <div class="duration-150 ease-in-out transform" x-state:on="Expanded" x-state:off="Collapsed" :class="{ 'rotate-90': open, '': !(open) }"> <i class="fa-regular fa-chevron-right"></i> </div> </button> <div x-description="Expandable link section, show/hide based on state." class="" x-show="open" x-cloak> <ul class=""> <li class="dropdown-item sub-menu-list-item text-gray-800"> <a href="/awards/awards-recognitions" class="menu-item-link flex px-6 py-3 font-semibold text-gray-900 hover__text-gray-500 border-l-16 border-primary-200 ml-2 rounded-lg my-1 focus__text-gray-500 hover__bg-gray-50 no-underline link-underline" data-drupal-link-system-path="node/1406">About Awards & Recognitions Program</a> </li> </ul> </div> </div> </li> <li class="dropdown-item sub-menu-list-item text-gray-800 expanded nav-item nav-item expanded nav-item has-sub-menu nav-item"> <div x-data="{ open: false }" x-title="Slide-over menu - Council Awards"> <button type="button" class="flex items-center justify-between w-full px-6 py-3 text-left text-gray-900 transition-colors duration-150 ease-in-out border-l-8 hover__text-gray-500 hover__bg-gray-100 focus__text-gray-500 focus__bg-gray-50 bg-gray-50 border-primary-400 ml-1 group focus__outline-none" x-state:on="Current" x-state:off="Default" @click="open = !open" aria-expanded="false" x-bind:aria-expanded="open.toString()" x-state-description=""> <span class="heading--nav--second-level menu-item-link inline-flex text-base mb-0 font-bold">Council Awards</span> <div class="duration-150 ease-in-out transform" x-state:on="Expanded" x-state:off="Collapsed" :class="{ 'rotate-90': open, '': !(open) }"> <i class="fa-regular fa-chevron-right"></i> </div> </button> <div x-description="Expandable link section, show/hide based on state." class="" x-show="open" x-cloak> <ul class=""> <li class="dropdown-item sub-menu-list-item text-gray-800"> <a href="/award/ceda-chapter-year-award" class="menu-item-link flex px-6 py-3 font-semibold text-gray-900 hover__text-gray-500 border-l-16 border-primary-200 ml-2 rounded-lg my-1 focus__text-gray-500 hover__bg-gray-50 no-underline link-underline" data-drupal-link-system-path="node/2130">Chapter of the Year</a> </li> <li class="dropdown-item sub-menu-list-item text-gray-800"> <a href="/awards/distinguished-service-award" class="menu-item-link flex px-6 py-3 font-semibold text-gray-900 hover__text-gray-500 border-l-16 border-primary-200 ml-2 rounded-lg my-1 focus__text-gray-500 hover__bg-gray-50 no-underline link-underline" data-drupal-link-system-path="node/17">Distinguished Service Award</a> </li> <li class="dropdown-item sub-menu-list-item text-gray-800"> <a href="/awards/kuh-early-career-award" class="menu-item-link flex px-6 py-3 font-semibold text-gray-900 hover__text-gray-500 border-l-16 border-primary-200 ml-2 rounded-lg my-1 focus__text-gray-500 hover__bg-gray-50 no-underline link-underline" data-drupal-link-system-path="node/18">Ernest S. Kuh Early Career Award</a> </li> <li class="dropdown-item sub-menu-list-item text-gray-800"> <a href="/awards/phil-kaufman-award" class="menu-item-link flex px-6 py-3 font-semibold text-gray-900 hover__text-gray-500 border-l-16 border-primary-200 ml-2 rounded-lg my-1 focus__text-gray-500 hover__bg-gray-50 no-underline link-underline">Phil Kaufman Award</a> </li> <li class="dropdown-item sub-menu-list-item text-gray-800"> <a href="/awards/phil-kaufman-hall-fame" class="menu-item-link flex px-6 py-3 font-semibold text-gray-900 hover__text-gray-500 border-l-16 border-primary-200 ml-2 rounded-lg my-1 focus__text-gray-500 hover__bg-gray-50 no-underline link-underline">Phil Kaufman Hall of Fame</a> </li> </ul> </div> </div> </li> <li class="dropdown-item sub-menu-list-item text-gray-800 expanded nav-item nav-item expanded nav-item has-sub-menu nav-item"> <div x-data="{ open: false }" x-title="Slide-over menu - Publications Awards"> <button type="button" class="flex items-center justify-between w-full px-6 py-3 text-left text-gray-900 transition-colors duration-150 ease-in-out border-l-8 hover__text-gray-500 hover__bg-gray-100 focus__text-gray-500 focus__bg-gray-50 bg-gray-50 border-primary-400 ml-1 group focus__outline-none" x-state:on="Current" x-state:off="Default" @click="open = !open" aria-expanded="false" x-bind:aria-expanded="open.toString()" x-state-description=""> <span class="heading--nav--second-level menu-item-link inline-flex text-base mb-0 font-bold">Publications Awards</span> <div class="duration-150 ease-in-out transform" x-state:on="Expanded" x-state:off="Collapsed" :class="{ 'rotate-90': open, '': !(open) }"> <i class="fa-regular fa-chevron-right"></i> </div> </button> <div x-description="Expandable link section, show/hide based on state." class="" x-show="open" x-cloak> <ul class=""> <li class="dropdown-item sub-menu-list-item text-gray-800"> <a href="/awards/a-richard-newton-award" class="menu-item-link flex px-6 py-3 font-semibold text-gray-900 hover__text-gray-500 border-l-16 border-primary-200 ml-2 rounded-lg my-1 focus__text-gray-500 hover__bg-gray-50 no-underline link-underline" data-drupal-link-system-path="node/19">A. Richard Newton Award</a> </li> <li class="dropdown-item sub-menu-list-item text-gray-800"> <a href="/awards/donald-o-pederson-award" class="menu-item-link flex px-6 py-3 font-semibold text-gray-900 hover__text-gray-500 border-l-16 border-primary-200 ml-2 rounded-lg my-1 focus__text-gray-500 hover__bg-gray-50 no-underline link-underline" data-drupal-link-system-path="node/20">Donald O. Pederson Award</a> </li> </ul> </div> </div> </li> <li class="dropdown-item sub-menu-list-item text-gray-800 expanded nav-item nav-item expanded nav-item has-sub-menu nav-item"> <div x-data="{ open: false }" x-title="Slide-over menu - Conference Awards"> <button type="button" class="flex items-center justify-between w-full px-6 py-3 text-left text-gray-900 transition-colors duration-150 ease-in-out border-l-8 hover__text-gray-500 hover__bg-gray-100 focus__text-gray-500 focus__bg-gray-50 bg-gray-50 border-primary-400 ml-1 group focus__outline-none" x-state:on="Current" x-state:off="Default" @click="open = !open" aria-expanded="false" x-bind:aria-expanded="open.toString()" x-state-description=""> <span class="heading--nav--second-level menu-item-link inline-flex text-base mb-0 font-bold">Conference Awards</span> <div class="duration-150 ease-in-out transform" x-state:on="Expanded" x-state:off="Collapsed" :class="{ 'rotate-90': open, '': !(open) }"> <i class="fa-regular fa-chevron-right"></i> </div> </button> <div x-description="Expandable link section, show/hide based on state." class="" x-show="open" x-cloak> <ul class=""> <li class="dropdown-item sub-menu-list-item text-gray-800"> <a href="/awards/outstanding-service-recognition" class="menu-item-link flex px-6 py-3 font-semibold text-gray-900 hover__text-gray-500 border-l-16 border-primary-200 ml-2 rounded-lg my-1 focus__text-gray-500 hover__bg-gray-50 no-underline link-underline" data-drupal-link-system-path="node/21">Outstanding Service Recognition</a> </li> <li class="dropdown-item sub-menu-list-item text-gray-800"> <a href="/awards/william-j-mccalla-award" class="menu-item-link flex px-6 py-3 font-semibold text-gray-900 hover__text-gray-500 border-l-16 border-primary-200 ml-2 rounded-lg my-1 focus__text-gray-500 hover__bg-gray-50 no-underline link-underline">William J McCalla Award</a> </li> </ul> </div> </div> </li> <li class="dropdown-item sub-menu-list-item text-gray-800 expanded nav-item nav-item expanded nav-item has-sub-menu nav-item"> <div x-data="{ open: false }" x-title="Slide-over menu - IEEE Awards"> <button type="button" class="flex items-center justify-between w-full px-6 py-3 text-left text-gray-900 transition-colors duration-150 ease-in-out border-l-8 hover__text-gray-500 hover__bg-gray-100 focus__text-gray-500 focus__bg-gray-50 bg-gray-50 border-primary-400 ml-1 group focus__outline-none" x-state:on="Current" x-state:off="Default" @click="open = !open" aria-expanded="false" x-bind:aria-expanded="open.toString()" x-state-description=""> <span class="heading--nav--second-level menu-item-link inline-flex text-base mb-0 font-bold">IEEE Awards</span> <div class="duration-150 ease-in-out transform" x-state:on="Expanded" x-state:off="Collapsed" :class="{ 'rotate-90': open, '': !(open) }"> <i class="fa-regular fa-chevron-right"></i> </div> </button> <div x-description="Expandable link section, show/hide based on state." class="" x-show="open" x-cloak> <ul class=""> <li class="dropdown-item sub-menu-list-item text-gray-800"> <a href="/awards/ieee-fellows" class="menu-item-link flex px-6 py-3 font-semibold text-gray-900 hover__text-gray-500 border-l-16 border-primary-200 ml-2 rounded-lg my-1 focus__text-gray-500 hover__bg-gray-50 no-underline link-underline" data-drupal-link-system-path="node/23">Fellows</a> </li> </ul> </div> </div> </li> </ul> </div> </div> </li> <li class="nav-item nav-item expanded nav-item nav-item expanded nav-item has-sub-menu nav-item"> <div x-data="{ open: false }" x-title="Slide-over menu - Activities"> <button type="button" class="flex items-center justify-between w-full px-6 py-3 text-left transition-colors duration-150 ease-in-out group focus__outline-none" x-state:on="Current" x-state:off="Default" @click="open = !open" aria-expanded="false" x-bind:aria-expanded="open.toString()" x-state-description="" :class="{ 'hover__text-gray-500 hover__bg-gray-50 focus__bg-gray-50' : !(open), 'hover__text-gray-50 bg-primary-600 text-white' : open }"> <span class="menu-item-link inline-flex no-underline font-bold">Activities</span> <div class="duration-150 ease-in-out transform" x-state:on="Expanded" x-state:off="Collapsed" :class="{ 'rotate-90': open, '': !(open) }"> <i class="fa-regular fa-chevron-right"></i> </div> </button> <div x-description="Expandable link section, show/hide based on state." class="" x-show="open" x-cloak> <ul class=""> <li class="dropdown-item sub-menu-list-item text-gray-800 expanded nav-item nav-item expanded nav-item has-sub-menu nav-item"> <div x-data="{ open: false }" x-title="Slide-over menu - Education"> <button type="button" class="flex items-center justify-between w-full px-6 py-3 text-left text-gray-900 transition-colors duration-150 ease-in-out border-l-8 hover__text-gray-500 hover__bg-gray-100 focus__text-gray-500 focus__bg-gray-50 bg-gray-50 border-primary-400 ml-1 group focus__outline-none" x-state:on="Current" x-state:off="Default" @click="open = !open" aria-expanded="false" x-bind:aria-expanded="open.toString()" x-state-description=""> <span class="heading--nav--second-level menu-item-link inline-flex text-base mb-0 font-bold">Education</span> <div class="duration-150 ease-in-out transform" x-state:on="Expanded" x-state:off="Collapsed" :class="{ 'rotate-90': open, '': !(open) }"> <i class="fa-regular fa-chevron-right"></i> </div> </button> <div x-description="Expandable link section, show/hide based on state." class="" x-show="open" x-cloak> <ul class=""> <li class="dropdown-item sub-menu-list-item text-gray-800"> <a href="/activities/distinguished-lecturers-program" class="menu-item-link flex px-6 py-3 font-semibold text-gray-900 hover__text-gray-500 border-l-16 border-primary-200 ml-2 rounded-lg my-1 focus__text-gray-500 hover__bg-gray-50 no-underline link-underline" data-drupal-link-system-path="node/1632">Distinguished Lecturer Program</a> </li> <li class="dropdown-item sub-menu-list-item text-gray-800"> <a href="/distinguished-lecturers-program/virtual-dlp" class="menu-item-link flex px-6 py-3 font-semibold text-gray-900 hover__text-gray-500 border-l-16 border-primary-200 ml-2 rounded-lg my-1 focus__text-gray-500 hover__bg-gray-50 no-underline link-underline" data-drupal-link-system-path="node/1748">Virtual Distinguished Lecturer Program</a> </li> <li class="dropdown-item sub-menu-list-item text-gray-800"> <a href="/activities/cad_for_assurance" class="menu-item-link flex px-6 py-3 font-semibold text-gray-900 hover__text-gray-500 border-l-16 border-primary-200 ml-2 rounded-lg my-1 focus__text-gray-500 hover__bg-gray-50 no-underline link-underline" data-drupal-link-system-path="node/1749">CAD for Assurance</a> </li> <li class="dropdown-item sub-menu-list-item text-gray-800"> <a href="/activities/dawn-webinars" class="menu-item-link flex px-6 py-3 font-semibold text-gray-900 hover__text-gray-500 border-l-16 border-primary-200 ml-2 rounded-lg my-1 focus__text-gray-500 hover__bg-gray-50 no-underline link-underline" data-drupal-link-system-path="node/1752">Design Automation Webinars</a> </li> </ul> </div> </div> </li> <li class="dropdown-item sub-menu-list-item text-gray-800 expanded nav-item nav-item expanded nav-item has-sub-menu nav-item"> <div x-data="{ open: false }" x-title="Slide-over menu - Chapters"> <button type="button" class="flex items-center justify-between w-full px-6 py-3 text-left text-gray-900 transition-colors duration-150 ease-in-out border-l-8 hover__text-gray-500 hover__bg-gray-100 focus__text-gray-500 focus__bg-gray-50 bg-gray-50 border-primary-400 ml-1 group focus__outline-none" x-state:on="Current" x-state:off="Default" @click="open = !open" aria-expanded="false" x-bind:aria-expanded="open.toString()" x-state-description=""> <span class="heading--nav--second-level menu-item-link inline-flex text-base mb-0 font-bold">Chapters</span> <div class="duration-150 ease-in-out transform" x-state:on="Expanded" x-state:off="Collapsed" :class="{ 'rotate-90': open, '': !(open) }"> <i class="fa-regular fa-chevron-right"></i> </div> </button> <div x-description="Expandable link section, show/hide based on state." class="" x-show="open" x-cloak> <ul class=""> <li class="dropdown-item sub-menu-list-item text-gray-800"> <a href="/activities/chapters" class="menu-item-link flex px-6 py-3 font-semibold text-gray-900 hover__text-gray-500 border-l-16 border-primary-200 ml-2 rounded-lg my-1 focus__text-gray-500 hover__bg-gray-50 no-underline link-underline" data-drupal-link-system-path="node/1777">Chapter Listings</a> </li> <li class="dropdown-item sub-menu-list-item text-gray-800"> <a href="/activities/chapters/chapter-resources" class="menu-item-link flex px-6 py-3 font-semibold text-gray-900 hover__text-gray-500 border-l-16 border-primary-200 ml-2 rounded-lg my-1 focus__text-gray-500 hover__bg-gray-50 no-underline link-underline" data-drupal-link-system-path="node/1779">Chapter Resources</a> </li> </ul> </div> </div> </li> <li class="dropdown-item sub-menu-list-item text-gray-800 expanded nav-item nav-item expanded nav-item has-sub-menu nav-item"> <div x-data="{ open: false }" x-title="Slide-over menu - Students and YP"> <button type="button" class="flex items-center justify-between w-full px-6 py-3 text-left text-gray-900 transition-colors duration-150 ease-in-out border-l-8 hover__text-gray-500 hover__bg-gray-100 focus__text-gray-500 focus__bg-gray-50 bg-gray-50 border-primary-400 ml-1 group focus__outline-none" x-state:on="Current" x-state:off="Default" @click="open = !open" aria-expanded="false" x-bind:aria-expanded="open.toString()" x-state-description=""> <span class="heading--nav--second-level menu-item-link inline-flex text-base mb-0 font-bold">Students and YP</span> <div class="duration-150 ease-in-out transform" x-state:on="Expanded" x-state:off="Collapsed" :class="{ 'rotate-90': open, '': !(open) }"> <i class="fa-regular fa-chevron-right"></i> </div> </button> <div x-description="Expandable link section, show/hide based on state." class="" x-show="open" x-cloak> <ul class=""> <li class="dropdown-item sub-menu-list-item text-gray-800"> <a href="/activities/students" class="menu-item-link flex px-6 py-3 font-semibold text-gray-900 hover__text-gray-500 border-l-16 border-primary-200 ml-2 rounded-lg my-1 focus__text-gray-500 hover__bg-gray-50 no-underline link-underline" data-drupal-link-system-path="node/1869">Students</a> </li> <li class="dropdown-item sub-menu-list-item text-gray-800"> <a href="/activities/students/student-travel-grant-program" class="menu-item-link flex px-6 py-3 font-semibold text-gray-900 hover__text-gray-500 border-l-16 border-primary-200 ml-2 rounded-lg my-1 focus__text-gray-500 hover__bg-gray-50 no-underline link-underline" data-drupal-link-system-path="node/1870">Student Travel Program</a> </li> <li class="dropdown-item sub-menu-list-item text-gray-800"> <a href="/activities/young-professionals" class="menu-item-link flex px-6 py-3 font-semibold text-gray-900 hover__text-gray-500 border-l-16 border-primary-200 ml-2 rounded-lg my-1 focus__text-gray-500 hover__bg-gray-50 no-underline link-underline" data-drupal-link-system-path="node/1875">Young Professionals</a> </li> </ul> </div> </div> </li> <li class="dropdown-item sub-menu-list-item text-gray-800 expanded nav-item nav-item expanded nav-item has-sub-menu nav-item"> <div x-data="{ open: false }" x-title="Slide-over menu - 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</div> </li> </ul> </nav> </div> </div> </div> </div> </div> </div> <div class="flex flex-col min-h-screen"> <div class="flex flex-col flex-grow pt-20 lg__flex-row lg__pt-30"> <main role="main" class="relative flex-auto bg-gray-50 --main "> <a id="main-content" tabindex="-1"></a> <div class="absolute flex w-full h-full bg-primary-500 bg-liquid-cheese max-h-40 min-h-40"></div> <div class="relative sm__-mb-10 z-10"> <div id="block-catalyze-tw-breadcrumbs" class="block block-system block-system-breadcrumb-block"> <section id="breadcrumbs" class="relative block bg-black bg-opacity-75" role="region"> <nav class="flex h-10 mx-auto " aria-label="Breadcrumb" role="navigation" aria-labelledby="system-breadcrumb"> <h2 id="system-breadcrumb" class="visually-hidden">Breadcrumb</h2> <ul class="container inline-flex"> <li class="inline-flex items-center group"> <a href="/" class="inline-flex items-center flex-shrink-0 h-full text-white group-hover__text-gray-200" title="Home"> <i class="fa-regular 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field--type-string field--label-visually_hidden full--visually_hidden break-words inline-flex font-bold" title="Ending page"> <span>798</span> </div> </div> </div> </div> </div> <div class="text-gray-500"> <div class="label font-normal inline-flex" title="Publication Date">Publication Date:</div> <div class="inline-flex ml-2 font-bold"> <div class="field field--media--field-date field--name-field-date field--type-datetime field--label-visually_hidden full--visually_hidden"> <div class="label field--label visually-hidden" title="Publication Date">Publication Date</div> <div title="Publication Date">June 1999</div> </div> </div> </div> <div class="pt-4 space-y-3"> <div class="field field--media--field-author-ref field--name-field-author-ref field--type-entity-reference field--label-visually_hidden full--visually_hidden"> <div class="label field--label visually-hidden">Author(s)</div> <div> <a href="/contact/chris-chu" hreflang="en">Chris Chu</a>; <a href="/contact/martin-df-wong" hreflang="en">Martin D.F. Wong</a> </div> </div> </div> </div> </div> </div> </header> <div class="grid grid-cols-1 mx-auto lg__grid-flow-col-dense lg__grid-cols-3"> <div class="tab--wrapper lg__col-start-1 lg__col-span-2 lg__border-separator-r" x-data="{ tab: window.location.hash ? window.location.hash.substring(1) : 'about', activeClasses: 'active text-primary-600', inactiveClasses: 'hover__text-gray-500', openMenu: false }">  <div class="flex items-center justify-between border-separator-b"> <h2 class="px-6 py-3 text-base capitalize lg__hidden">paper Menu</h2> <button type="button" class="block h-full px-6 py-3 mb-0 lg__hidden focus__outline-none" @click="openMenu = !openMenu" aria-label="Menu"> <i class="fa-regular fa-bars fa-lg"></i> </button> </div> <div class="lg__mx-0 lg__px-6 border-separator-b"> <nav class="flex-col w-full divide-y lg__flex lg__flex-row tab--nav lg__divide-y-0" x-show="openMenu" x-cloak :class="{ 'flex' : openMenu, '' : !openMenu }"> <a class="tab--link relative px-6 lg__px-3 py-3 lg__first__pl-0 lg__last__pr-0 font-bold hover__after__left-0 hover__after__right-0 focus__outline-none after__bg-primary-500 after__h-1 lg__after__absolute after__bottom-0 after__duration-150 after__transition-all after__ease-in-out after__left-full after__right-0 content-after" :class="tab === 'about' ? activeClasses : inactiveClasses" @click.prevent="tab = 'about'; window.location.hash = 'about'" href="#" title="About"> <i class="mr-2 fa-regular fa-fw fa-info-circle"></i>About</a> <a class="tab--link relative px-6 lg__px-3 py-3 lg__first__pl-0 lg__last__pr-0 font-bold hover__after__left-0 hover__after__right-0 focus__outline-none after__bg-primary-500 after__h-1 lg__after__absolute after__bottom-0 after__duration-150 after__transition-all after__ease-in-out after__left-full after__right-0 content-after" :class="tab === 'authors' ? activeClasses : inactiveClasses" @click.prevent="tab = 'authors'; window.location.hash = 'authors'" href="#" title="Authors"> <i class="mr-2 fa-regular fa-fw fa-user-group"></i>Authors</a> </nav> </div>  <div class="tab--content p-6 space-y-6" x-show="tab === 'about'"> <div class="label field--label">Abstract</div> <div class="mx-auto break-words word-wrap prose font-serif relative"> <p>In this paper, we present a completely new approach to the problem of delay minimization by simultaneous buffer insertion and wire sizing for a wire. We show that the problem can be formulated as a convex quadratic program, which is known to be solvable in polynomial time. Nevertheless, we explore some special properties of our problem and derive an optimal and very efficient algorithm, modified active set method (MASM), to solve the resulting program. Given m buffers and a set of m discrete choices of wire width, the running time of our algorithm is O(mn/sup 2/) and is independent of the wire length in practice. For example, an instance of 100 buffers and 100 choices of wire width can be solved in 0.92 s. In addition, we extend MASM to consider simultaneous buffer insertion, buffer sizing, and wire sizing. The resulting algorithm MASM-BS is again optimal and very efficient. For example, with six choices of buffer size and 10 choices of wire width, the optimal solution for a 15000 /spl mu/m long wire can be found in 0.05 s. Besides, our formulation is so versatile that it is easy to consider other objectives like wire area or power dissipation, or to add constraints to the solution. Also, wire capacitance lookup tables, or very general wire capacitance models which can capture area capacitance, fringing capacitance, coupling capacitance, etc. can be used.</p> </div> </div> <div class="tab--content p-6 space-y-6" x-show="tab === 'authors'"> <div class="grid grid-cols-2 gap-8"> <article about="/contact/chris-chu" data-observe-resizes="" class="responsive-container w-full card--container flex flex-col"> <div class="flex card-v xl__card-h card card--contact overflow-hidden"> <div class="card--header card-v--header xl__card-h--header bg-gray-50 relative flex-shrink-0 flex"> <a href="/contact/chris-chu"> <img class="lazyload" src="https://ui-avatars.com/api/?size=500&name=Chris Chu" alt=""> </a> </div> <div class="card--main xl__card-h--main flex flex-col justify-between"> <div class="card--body xl__card-h--body px-6 py-3"> <div class="inline-flex flex-wrap items-end space-x-1 align-baseline"> <div> <div class="label field--label visually-hidden"></div> <h3 class="field field--node--field-display-title field--name-field-display-title field--type-string field--label-visually_hidden card--visually_hidden text-base leading-tight line-clamp-4 hover__line-clamp-none focus-within__line-clamp-none" title="Chris Chu "> <span><a href="/contact/chris-chu" hreflang="en">Chris Chu</a></span> </h3> </div> </div> <div class="mt-1"> </div> </div> </div> </div> </article> <article about="/contact/martin-df-wong" data-observe-resizes="" class="responsive-container w-full card--container flex flex-col"> <div class="flex card-v xl__card-h card card--contact overflow-hidden"> <div class="card--header card-v--header xl__card-h--header bg-gray-50 relative flex-shrink-0 flex"> <a href="/contact/martin-df-wong"> <img class="lazyload" src="https://ui-avatars.com/api/?size=500&name=Martin D.F. Wong" alt=""> </a> </div> <div class="card--main xl__card-h--main flex flex-col justify-between"> <div class="card--body xl__card-h--body px-6 py-3"> <div class="inline-flex flex-wrap items-end space-x-1 align-baseline"> <div> <div class="label field--label visually-hidden"></div> <h3 class="field field--node--field-display-title field--name-field-display-title field--type-string field--label-visually_hidden card--visually_hidden text-base leading-tight line-clamp-4 hover__line-clamp-none focus-within__line-clamp-none" title="Martin D.F. Wong "> <span><a href="/contact/martin-df-wong" hreflang="en">Martin D.F. 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A quadratic programming approach to simultaneous buffer insertion/sizing and wire sizing | IEEE CEDA