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class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 13 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-13" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">13 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AA%D9%83%D8%A7%D9%85%D9%84_%D8%A7%D9%84%D8%A8%D9%8A%D8%A7%D9%86%D8%A7%D8%AA" title="تكامل البيانات – Arabic" lang="ar" hreflang="ar" data-title="تكامل البيانات" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Integreiddio_data" title="Integreiddio data – Welsh" lang="cy" hreflang="cy" data-title="Integreiddio data" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Informationsintegration" title="Informationsintegration – German" lang="de" hreflang="de" data-title="Informationsintegration" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A7%D8%AF%D8%BA%D8%A7%D9%85_%D8%AF%D8%A7%D8%AF%D9%87" title="ادغام داده – Persian" lang="fa" hreflang="fa" data-title="ادغام داده" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Consolidation_informatique" title="Consolidation informatique – French" lang="fr" hreflang="fr" data-title="Consolidation informatique" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Data_integration" title="Data integration – Italian" lang="it" hreflang="it" data-title="Data integration" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9C%D3%99%D0%BB%D1%96%D0%BC%D0%B5%D1%82%D1%82%D0%B5%D1%80%D0%B4%D1%96_%D0%B0%D0%BB%D0%BC%D0%B0%D1%81%D1%82%D1%8B%D1%80%D1%83" title="Мәліметтерді алмастыру – Kazakh" lang="kk" hreflang="kk" data-title="Мәліметтерді алмастыру" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Data-integratie" title="Data-integratie – Dutch" lang="nl" hreflang="nl" data-title="Data-integratie" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Dataintegrasjon" title="Dataintegrasjon – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Dataintegrasjon" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%98%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B0%D1%86%D0%B8%D1%8F_%D0%B4%D0%B0%D0%BD%D0%BD%D1%8B%D1%85" title="Интеграция данных – Russian" lang="ru" hreflang="ru" data-title="Интеграция данных" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Dataintegraatio" title="Dataintegraatio – Finnish" lang="fi" hreflang="fi" data-title="Dataintegraatio" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/T%C3%ADch_h%E1%BB%A3p_d%E1%BB%AF_li%E1%BB%87u" title="Tích hợp dữ liệu – Vietnamese" lang="vi" hreflang="vi" data-title="Tích hợp dữ liệu" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" 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<div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Combining data from multiple sources</div> <p><b>Data integration</b> refers to the process of combining, sharing, or synchronizing <a href="/wiki/Data" title="Data">data</a> from multiple sources to provide users with a unified view.<sup id="cite_ref-refone_1-0" class="reference"><a href="#cite_note-refone-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> There are a wide range of possible applications for data integration, from commercial (such as when a business merges multiple <a href="/wiki/Database" title="Database">databases</a>) to scientific (combining research data from different <a href="/wiki/Bioinformatics" title="Bioinformatics">bioinformatics</a> repositories). </p><p>The decision to integrate data tends to arise when the volume, complexity (that is, <a href="/wiki/Big_data" title="Big data">big data</a>) and need to share existing data <a href="/wiki/Information_explosion" title="Information explosion">explodes</a>.<sup id="cite_ref-DataExplode_2-0" class="reference"><a href="#cite_note-DataExplode-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> It has become the focus of extensive theoretical work, and numerous open problems remain unsolved. </p><p>Data integration encourages collaboration between internal as well as external users. The data being integrated must be received from a <a href="/wiki/Heterogeneous_database_system" title="Heterogeneous database system">heterogeneous database system</a> and transformed to a single coherent data store that provides synchronous data across a network of files for clients.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> A common use of data integration is in <a href="/wiki/Data_mining" title="Data mining">data mining</a> when analyzing and extracting information from existing databases that can be useful for <a href="/wiki/Business_information" class="mw-redirect" title="Business information">Business information</a>.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Data_integration&action=edit&section=1" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Datawarehouse.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/db/Datawarehouse.png/220px-Datawarehouse.png" decoding="async" width="220" height="148" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/db/Datawarehouse.png/330px-Datawarehouse.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/db/Datawarehouse.png/440px-Datawarehouse.png 2x" data-file-width="963" data-file-height="648" /></a><figcaption>Figure 1: Simple schematic for a data warehouse. The <a href="/wiki/Extract,_transform,_load" title="Extract, transform, load">Extract, transform, load</a> (ETL) process extracts information from the source databases, transforms it and then loads it into the data warehouse.</figcaption></figure> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Dataintegration.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Dataintegration.png/220px-Dataintegration.png" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Dataintegration.png/330px-Dataintegration.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Dataintegration.png/440px-Dataintegration.png 2x" data-file-width="1024" data-file-height="768" /></a><figcaption>Figure 2: Simple schematic for a data-integration solution. A system designer constructs a mediated schema against which users can run queries. The <a href="/wiki/Virtual_database" class="mw-redirect" title="Virtual database">virtual database</a> interfaces with the source databases via <a href="/wiki/Wrapper_pattern" class="mw-redirect" title="Wrapper pattern">wrapper</a> code if required.</figcaption></figure> <p>Issues with combining <a href="/wiki/Heterogeneous" class="mw-redirect" title="Heterogeneous">heterogeneous</a> data sources, often referred to as <a href="/wiki/Information_silo" title="Information silo">information silos</a>, under a single query interface have existed for some time. In the early 1980s, computer scientists began designing systems for interoperability of heterogeneous databases.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>The first data integration system driven by structured metadata was designed in 1991 at the <a href="/wiki/University_of_Minnesota" title="University of Minnesota">University of Minnesota</a> for the <a href="/wiki/IPUMS" title="IPUMS">Integrated Public Use Microdata Series (IPUMS)</a>. IPUMS used a <a href="/wiki/Data_warehousing" class="mw-redirect" title="Data warehousing">data warehousing</a> approach, which <a href="/wiki/Extract,_transform,_load" title="Extract, transform, load">extracts, transforms, and loads</a> data from heterogeneous sources into a unique view <a href="/wiki/Logical_schema" title="Logical schema">schema</a> so data from different sources become compatible.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> By making thousands of population databases interoperable, IPUMS demonstrated the feasibility of large-scale data integration. The data warehouse approach offers a <a href="/wiki/Coupling_(computer_science)" class="mw-redirect" title="Coupling (computer science)">tightly coupled</a> architecture because the data are already physically reconciled in a single queryable repository, so it usually takes little time to resolve queries.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><p>The <a href="/wiki/Data_warehouse" title="Data warehouse">data warehouse</a> approach is less feasible for data sets that are frequently updated, requiring the <a href="/wiki/Extract,_transform,_load" title="Extract, transform, load">extract, transform, load</a> (ETL) process to be continuously re-executed for synchronization. Difficulties also arise in constructing data warehouses when one has only a query interface to summary data sources and no access to the full data. This problem frequently emerges when integrating several commercial query services like travel or classified advertisement web applications. </p><p>A trend began in 2009 favoring the <a href="/wiki/Loose_coupling" title="Loose coupling">loose coupling</a> of data<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> and providing a unified query-interface to access real time data over a <a href="/wiki/Data_mediation" class="mw-redirect" title="Data mediation">mediated</a> schema (see Figure 2), which allows information to be retrieved directly from original databases. This is consistent with the <a href="/wiki/Service-oriented_architecture" title="Service-oriented architecture">SOA</a> approach popular in that era. This approach relies on mappings between the mediated schema and the schema of original sources, and translating a query into decomposed queries to match the schema of the original databases. Such mappings can be specified in two ways: as a mapping from entities in the mediated schema to entities in the original sources (the "Global-as-View"<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> (GAV) approach), or as a mapping from entities in the original sources to the mediated schema (the "Local-as-View"<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> (LAV) approach). The latter approach requires more sophisticated inferences to resolve a query on the mediated schema, but makes it easier to add new data sources to a (stable) mediated schema. </p><p>As of 2010<sup class="plainlinks noexcerpt noprint asof-tag update" style="display:none;"><a class="external text" href="https://en.wikipedia.org/w/index.php?title=Data_integration&action=edit">[update]</a></sup>, some of the work in data integration research concerns the <a href="/wiki/Semantic_integration" title="Semantic integration">semantic integration</a> problem. This problem addresses not the structuring of the architecture of the integration, but how to resolve <a href="/wiki/Semantic" class="mw-redirect" title="Semantic">semantic</a> conflicts between heterogeneous data sources. For example, if two companies merge their databases, certain concepts and definitions in their respective schemas like "earnings" inevitably have different meanings. In one database it may mean profits in dollars (a floating-point number), while in the other it might represent the number of sales (an integer). A common strategy for the resolution of such problems involves the use of <a href="/wiki/Ontology_(computer_science)" class="mw-redirect" title="Ontology (computer science)">ontologies</a> which explicitly define schema terms and thus help to resolve semantic conflicts. This approach represents <a href="/wiki/Ontology-based_data_integration" title="Ontology-based data integration">ontology-based data integration</a>. On the other hand, the problem of combining research results from different bioinformatics repositories requires bench-marking of the similarities, computed from different data sources, on a single criterion such as positive predictive value. This enables the data sources to be directly comparable and can be integrated even when the natures of experiments are distinct.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p>As of 2011<sup class="plainlinks noexcerpt noprint asof-tag update" style="display:none;"><a class="external text" href="https://en.wikipedia.org/w/index.php?title=Data_integration&action=edit">[update]</a></sup>, it was determined that current <a href="/wiki/Data_modeling" title="Data modeling">data modeling</a> methods were imparting data isolation into every <a href="/wiki/Data_architecture" title="Data architecture">data architecture</a> in the form of islands of disparate data and information silos. This data isolation is an unintended artifact of the data modeling methodology that results in the development of disparate data models. Disparate data models, when instantiated as databases, form disparate databases. Enhanced data model methodologies have been developed to eliminate the data isolation artifact and to promote the development of integrated data models.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> One enhanced data modeling method recasts data models by augmenting them with structural <a href="/wiki/Metadata" title="Metadata">metadata</a> in the form of standardized data entities. As a result of recasting multiple data models, the set of recast data models will now share one or more commonality relationships that relate the structural metadata now common to these data models. Commonality relationships are a peer-to-peer type of entity relationships that relate the standardized data entities of multiple data models. Multiple data models that contain the same standard data entity may participate in the same commonality relationship. When integrated data models are instantiated as databases and are properly populated from a common set of master data, then these databases are integrated. </p><p>Since 2011, <a href="/wiki/Data_hub" title="Data hub">data hub</a> approaches have been of greater interest than fully structured (typically relational) Enterprise Data Warehouses. Since 2013, <a href="/wiki/Data_lake" title="Data lake">data lake</a> approaches have risen to the level of Data Hubs. (See all three search terms popularity on Google Trends.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup>) These approaches combine unstructured or varied data into one location, but do not necessarily require an (often complex) master relational schema to structure and define all data in the Hub. </p><p>Data integration plays a big role in business regarding <a href="/wiki/Data_collection" title="Data collection">data collection</a> used for studying the market. Converting the raw data retrieved from consumers into coherent data is something businesses try to do when considering what steps they should take next.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> Organizations are more frequently using <a href="/wiki/Data_mining" title="Data mining">data mining</a> for collecting information and patterns from their databases, and this process helps them develop new business strategies to increase business performance and perform economic analyses more efficiently. Compiling the large amount of data they collect to be stored in their system is a form of data integration adapted for <a href="/wiki/Business_intelligence" title="Business intelligence">Business intelligence</a> to improve their chances of success.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Example">Example</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Data_integration&action=edit&section=2" title="Edit section: Example"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Consider a <a href="/wiki/Web_application" title="Web application">web application</a> where a user can query a variety of information about cities (such as crime statistics, weather, hotels, demographics, etc.). Traditionally, the information must be stored in a single database with a single schema. But any single enterprise would find information of this breadth somewhat difficult and expensive to collect. Even if the resources exist to gather the data, it would likely duplicate data in existing crime databases, weather websites, and census data. </p><p>A data-integration solution may address this problem by considering these external resources as <a href="/wiki/Materialized_view" title="Materialized view">materialized views</a> over a <a href="/wiki/Virtual_database" class="mw-redirect" title="Virtual database">virtual mediated schema</a>, resulting in "virtual data integration". This means application-developers construct a virtual schema—the <i>mediated schema</i>—to best model the kinds of answers their users want. Next, they design "wrappers" or adapters for each data source, such as the crime database and weather website. These adapters simply transform the local query results (those returned by the respective websites or databases) into an easily processed form for the data integration solution (see figure 2). When an application-user queries the mediated schema, the data-integration solution transforms this query into appropriate queries over the respective data sources. Finally, the virtual database combines the results of these queries into the answer to the user's query. </p><p>This solution offers the convenience of adding new sources by simply constructing an adapter or an application software blade for them. It contrasts with <a href="/wiki/Extract,_transform,_load" title="Extract, transform, load">ETL</a> systems or with a single database solution, which require manual integration of entire new data set into the system. The virtual ETL solutions leverage <a href="/wiki/Virtual_database" class="mw-redirect" title="Virtual database">virtual mediated schema</a> to implement data harmonization; whereby the data are copied from the designated "master" source to the defined targets, field by field. Advanced <a href="/wiki/Data_virtualization" title="Data virtualization">data virtualization</a> is also built on the concept of object-oriented modeling in order to construct virtual mediated schema or virtual metadata repository, using <a href="/wiki/Hub_and_spoke" class="mw-redirect" title="Hub and spoke">hub and spoke</a> architecture. </p><p>Each data source is disparate and as such is not designed to support reliable joins between data sources. Therefore, data virtualization as well as data federation depends upon accidental data commonality to support combining data and information from disparate data sets. Because of the lack of data value commonality across data sources, the return set may be inaccurate, incomplete, and impossible to validate. </p><p>One solution is to recast disparate databases to integrate these databases without the need for <a href="/wiki/Extract,_transform,_load" title="Extract, transform, load">ETL</a>. The recast databases support commonality constraints where referential integrity may be enforced between databases. The recast databases provide designed data access paths with data value commonality across databases. </p> <div class="mw-heading mw-heading2"><h2 id="Theory">Theory</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Data_integration&action=edit&section=3" title="Edit section: Theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The theory of data integration<sup id="cite_ref-refone_1-1" class="reference"><a href="#cite_note-refone-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> forms a subset of database theory and formalizes the underlying concepts of the problem in <a href="/wiki/First-order_logic" title="First-order logic">first-order logic</a>. Applying the theories gives indications as to the feasibility and difficulty of data integration. While its definitions may appear abstract, they have sufficient generality to accommodate all manner of integration systems,<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> including those that include nested relational / XML databases<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> and those that treat databases as programs.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> Connections to particular databases systems such as Oracle or DB2 are provided by implementation-level technologies such as <a href="/wiki/JDBC" class="mw-redirect" title="JDBC">JDBC</a> and are not studied at the theoretical level. </p> <div class="mw-heading mw-heading3"><h3 id="Definitions">Definitions</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Data_integration&action=edit&section=4" title="Edit section: Definitions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Data integration systems are formally defined as a <a href="/wiki/Tuple_(mathematics)" class="mw-redirect" title="Tuple (mathematics)">tuple</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left\langle G,S,M\right\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>⟨</mo> <mrow> <mi>G</mi> <mo>,</mo> <mi>S</mi> <mo>,</mo> <mi>M</mi> </mrow> <mo>⟩</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left\langle G,S,M\right\rangle }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7788300afd54ade3062e3518ec69ac307b1038d7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.645ex; height:2.843ex;" alt="{\displaystyle \left\langle G,S,M\right\rangle }"></span> where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5f3c8921a3b352de45446a6789b104458c9f90b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.827ex; height:2.176ex;" alt="{\displaystyle G}"></span> is the global (or mediated) schema, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span> is the heterogeneous set of source schemas, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle M}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f82cade9898ced02fdd08712e5f0c0151758a0dd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.442ex; height:2.176ex;" alt="{\displaystyle M}"></span> is the mapping that maps queries between the source and the global schemas. Both <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5f3c8921a3b352de45446a6789b104458c9f90b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.827ex; height:2.176ex;" alt="{\displaystyle G}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span> are expressed in <a href="/wiki/Formal_language" title="Formal language">languages</a> over <a href="/wiki/Alphabet_(computer_science)" class="mw-redirect" title="Alphabet (computer science)">alphabets</a> composed of symbols for each of their respective <a href="/wiki/Relational_database" title="Relational database">relations</a>. The <a href="/wiki/Functional_predicate" title="Functional predicate">mapping</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle M}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f82cade9898ced02fdd08712e5f0c0151758a0dd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.442ex; height:2.176ex;" alt="{\displaystyle M}"></span> consists of assertions between queries over <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5f3c8921a3b352de45446a6789b104458c9f90b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.827ex; height:2.176ex;" alt="{\displaystyle G}"></span> and queries over <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span>. When users pose queries over the data integration system, they pose queries over <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5f3c8921a3b352de45446a6789b104458c9f90b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.827ex; height:2.176ex;" alt="{\displaystyle G}"></span> and the mapping then asserts connections between the elements in the global schema and the source schemas. </p><p>A database over a schema is defined as a set of sets, one for each relation (in a relational database). The database corresponding to the source schema <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span> would comprise the set of sets of tuples for each of the heterogeneous data sources and is called the <i>source database</i>. Note that this single source database may actually represent a collection of disconnected databases. The database corresponding to the virtual mediated schema <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5f3c8921a3b352de45446a6789b104458c9f90b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.827ex; height:2.176ex;" alt="{\displaystyle G}"></span> is called the <i>global database</i>. The global database must satisfy the mapping <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle M}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f82cade9898ced02fdd08712e5f0c0151758a0dd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.442ex; height:2.176ex;" alt="{\displaystyle M}"></span> with respect to the source database. The legality of this mapping depends on the nature of the correspondence between <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5f3c8921a3b352de45446a6789b104458c9f90b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.827ex; height:2.176ex;" alt="{\displaystyle G}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span>. Two popular ways to model this correspondence exist: <i>Global as View</i> or GAV and <i>Local as View</i> or LAV. </p> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:GAVLAV.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9e/GAVLAV.png/220px-GAVLAV.png" decoding="async" width="220" height="108" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9e/GAVLAV.png/330px-GAVLAV.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9e/GAVLAV.png/440px-GAVLAV.png 2x" data-file-width="885" data-file-height="434" /></a><figcaption>Figure 3: Illustration of tuple space of the GAV and LAV mappings.<sup id="cite_ref-refseven_19-0" class="reference"><a href="#cite_note-refseven-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> In GAV, the system is constrained to the set of tuples mapped by the mediators while the set of tuples expressible over the sources may be much larger and richer. In LAV, the system is constrained to the set of tuples in the sources while the set of tuples expressible over the global schema can be much larger. Therefore, LAV systems must often deal with incomplete answers.</figcaption></figure> <p>GAV systems model the global database as a set of <a href="/wiki/View_(database)" class="mw-redirect" title="View (database)">views</a> over <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span>. In this case <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle M}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f82cade9898ced02fdd08712e5f0c0151758a0dd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.442ex; height:2.176ex;" alt="{\displaystyle M}"></span> associates to each element of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5f3c8921a3b352de45446a6789b104458c9f90b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.827ex; height:2.176ex;" alt="{\displaystyle G}"></span> a query over <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span>. <a href="/wiki/Query_optimizer" class="mw-redirect" title="Query optimizer">Query processing</a> becomes a straightforward operation due to the well-defined associations between <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5f3c8921a3b352de45446a6789b104458c9f90b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.827ex; height:2.176ex;" alt="{\displaystyle G}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span>. The burden of complexity falls on implementing mediator code instructing the data integration system exactly how to retrieve elements from the source databases. If any new sources join the system, considerable effort may be necessary to update the mediator, thus the GAV approach appears preferable when the sources seem unlikely to change. </p><p>In a GAV approach to the example data integration system above, the system designer would first develop mediators for each of the city information sources and then design the global schema around these mediators. For example, consider if one of the sources served a weather website. The designer would likely then add a corresponding element for weather to the global schema. Then the bulk of effort concentrates on writing the proper mediator code that will transform predicates on weather into a query over the weather website. This effort can become complex if some other source also relates to weather, because the designer may need to write code to properly combine the results from the two sources. </p><p>On the other hand, in LAV, the source database is modeled as a set of <a href="/wiki/View_(database)" class="mw-redirect" title="View (database)">views</a> over <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5f3c8921a3b352de45446a6789b104458c9f90b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.827ex; height:2.176ex;" alt="{\displaystyle G}"></span>. In this case <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle M}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f82cade9898ced02fdd08712e5f0c0151758a0dd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.442ex; height:2.176ex;" alt="{\displaystyle M}"></span> associates to each element of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span> a query over <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5f3c8921a3b352de45446a6789b104458c9f90b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.827ex; height:2.176ex;" alt="{\displaystyle G}"></span>. Here the exact associations between <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5f3c8921a3b352de45446a6789b104458c9f90b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.827ex; height:2.176ex;" alt="{\displaystyle G}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span> are no longer well-defined. As is illustrated in the next section, the burden of determining how to retrieve elements from the sources is placed on the query processor. The benefit of an LAV modeling is that new sources can be added with far less work than in a GAV system, thus the LAV approach should be favored in cases where the mediated schema is less stable or likely to change.<sup id="cite_ref-refone_1-2" class="reference"><a href="#cite_note-refone-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>In an LAV approach to the example data integration system above, the system designer designs the global schema first and then simply inputs the schemas of the respective city information sources. Consider again if one of the sources serves a weather website. The designer would add corresponding elements for weather to the global schema only if none existed already. Then programmers write an adapter or wrapper for the website and add a schema description of the website's results to the source schemas. The complexity of adding the new source moves from the designer to the query processor. </p> <div class="mw-heading mw-heading3"><h3 id="Query_processing">Query processing</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Data_integration&action=edit&section=5" title="Edit section: Query processing"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The theory of query processing in data integration systems is commonly expressed using conjunctive <a href="/wiki/Database_query_language" class="mw-redirect" title="Database query language">queries</a> and <a href="/wiki/Datalog" title="Datalog">Datalog</a>, a purely declarative <a href="/wiki/Logic_programming" title="Logic programming">logic programming</a> language.<sup id="cite_ref-reffive_20-0" class="reference"><a href="#cite_note-reffive-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> One can loosely think of a <a href="/wiki/Conjunctive_query" title="Conjunctive query">conjunctive query</a> as a logical function applied to the relations of a database such as "<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(A,B)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>A</mi> <mo>,</mo> <mi>B</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(A,B)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3f823b6f920a2513302ee807420d86eeeb142719" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.629ex; height:2.843ex;" alt="{\displaystyle f(A,B)}"></span> where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A<B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo><</mo> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A<B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8f7bff3eeb3cd93f23984f67cb4a10787de83596" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.606ex; height:2.176ex;" alt="{\displaystyle A<B}"></span>". If a tuple or set of tuples is substituted into the rule and satisfies it (makes it true), then we consider that tuple as part of the set of answers in the query. While formal languages like Datalog express these queries concisely and without ambiguity, common <a href="/wiki/SQL" title="SQL">SQL</a> queries count as conjunctive queries as well. </p><p>In terms of data integration, "query containment" represents an important property of conjunctive queries. A query <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> contains another query <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}"></span> (denoted <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A\supset B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>⊃</mo> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A\supset B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ee952838d8b3e67045072a8f2b71e7fc0467dea6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.606ex; height:2.176ex;" alt="{\displaystyle A\supset B}"></span>) if the results of applying <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}"></span> are a subset of the results of applying <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> for any database. The two queries are said to be equivalent if the resulting sets are equal for any database. This is important because in both GAV and LAV systems, a user poses conjunctive queries over a <i>virtual</i> schema represented by a set of <a href="/wiki/View_(database)" class="mw-redirect" title="View (database)">views</a>, or "materialized" conjunctive queries. Integration seeks to rewrite the queries represented by the views to make their results equivalent or maximally contained by our user's query. This corresponds to the problem of answering queries using views (<a href="/w/index.php?title=AQUV&action=edit&redlink=1" class="new" title="AQUV (page does not exist)">AQUV</a>).<sup id="cite_ref-refsix_21-0" class="reference"><a href="#cite_note-refsix-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </p><p>In GAV systems, a system designer writes mediator code to define the query-rewriting. Each element in the user's query corresponds to a substitution rule just as each element in the global schema corresponds to a query over the source. Query processing simply expands the subgoals of the user's query according to the rule specified in the mediator and thus the resulting query is likely to be equivalent. While the designer does the majority of the work beforehand, some GAV systems such as <a rel="nofollow" class="external text" href="http://www-db.stanford.edu/tsimmis/">Tsimmis</a> involve simplifying the mediator description process. </p><p>In LAV systems, queries undergo a more radical process of rewriting because no mediator exists to align the user's query with a simple expansion strategy. The integration system must execute a search over the space of possible queries in order to find the best rewrite. The resulting rewrite may not be an equivalent query but maximally contained, and the resulting tuples may be incomplete. As of 2011<sup class="plainlinks noexcerpt noprint asof-tag update" style="display:none;"><a class="external text" href="https://en.wikipedia.org/w/index.php?title=Data_integration&action=edit">[update]</a></sup> the GQR algorithm<sup id="cite_ref-refgqr_22-0" class="reference"><a href="#cite_note-refgqr-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> is the leading query rewriting algorithm for LAV data integration systems. </p><p>In general, the complexity of query rewriting is <a href="/wiki/NP-complete" class="mw-redirect" title="NP-complete">NP-complete</a>.<sup id="cite_ref-refsix_21-1" class="reference"><a href="#cite_note-refsix-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> If the space of rewrites is relatively small, this does not pose a problem — even for integration systems with hundreds of sources. </p> <div class="mw-heading mw-heading2"><h2 id="Medicine_and_life_sciences">Medicine and life sciences</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Data_integration&action=edit&section=6" title="Edit section: Medicine and life sciences"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Large-scale questions in science, such as <a href="/wiki/Real_world_evidence" title="Real world evidence">real world evidence</a>, <a href="/wiki/Global_warming" class="mw-redirect" title="Global warming">global warming</a>, <a href="/wiki/Invasive_species" title="Invasive species">invasive species</a> spread, and <a href="/wiki/Resource_depletion" title="Resource depletion">resource depletion</a>, are increasingly requiring the collection of disparate data sets for <a href="/wiki/Meta-analysis" title="Meta-analysis">meta-analysis</a>. This type of data integration is especially challenging for ecological and environmental data because <a href="/wiki/Metadata_standards" class="mw-redirect" title="Metadata standards">metadata standards</a> are not agreed upon and there are many different data types produced in these fields. <a href="/wiki/National_Science_Foundation" title="National Science Foundation">National Science Foundation</a> initiatives such as <a href="/wiki/Datanet" title="Datanet">Datanet</a> are intended to make data integration easier for scientists by providing <a href="/wiki/Cyberinfrastructure" title="Cyberinfrastructure">cyberinfrastructure</a> and setting standards. The five funded <a href="/wiki/Datanet" title="Datanet">Datanet</a> initiatives are <a href="/wiki/DataONE" title="DataONE">DataONE</a>,<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> led by William Michener at the <a href="/wiki/University_of_New_Mexico" title="University of New Mexico">University of New Mexico</a>; The Data Conservancy,<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> led by Sayeed Choudhury of <a href="/wiki/Johns_Hopkins_University" title="Johns Hopkins University">Johns Hopkins University</a>; SEAD: Sustainable Environment through Actionable Data,<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> led by <a href="/wiki/Margaret_Hedstrom" title="Margaret Hedstrom">Margaret Hedstrom</a> of the <a href="/wiki/University_of_Michigan" title="University of Michigan">University of Michigan</a>; the DataNet Federation Consortium,<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> led by Reagan Moore of the <a href="/wiki/University_of_North_Carolina" title="University of North Carolina">University of North Carolina</a>; and <i>Terra Populus</i>,<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> led by <a href="/wiki/Steven_Ruggles" title="Steven Ruggles">Steven Ruggles</a> of the <a href="/wiki/University_of_Minnesota" title="University of Minnesota">University of Minnesota</a>. The <a href="/wiki/Research_Data_Alliance" title="Research Data Alliance">Research Data Alliance</a>,<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> has more recently explored creating global data integration frameworks. The <a href="/wiki/OpenPHACTS" title="OpenPHACTS">OpenPHACTS</a> project, funded through the <a href="/wiki/European_Union" title="European Union">European Union</a> <a href="/wiki/Innovative_Medicines_Initiative" title="Innovative Medicines Initiative">Innovative Medicines Initiative</a>, built a drug discovery platform by linking datasets from providers such as <a href="/wiki/European_Bioinformatics_Institute" title="European Bioinformatics Institute">European Bioinformatics Institute</a>, <a href="/wiki/Royal_Society_of_Chemistry" title="Royal Society of Chemistry">Royal Society of Chemistry</a>, <a href="/wiki/UniProt" title="UniProt">UniProt</a>, <a href="/wiki/WikiPathways" title="WikiPathways">WikiPathways</a> and <a href="/wiki/DrugBank" title="DrugBank">DrugBank</a>. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Data_integration&action=edit&section=7" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 20em;"> <ul><li><a href="/wiki/Business_semantics_management" title="Business semantics management">Business semantics management</a></li> <li><a href="/wiki/Change_data_capture" title="Change data capture">Change data capture</a></li> <li><a href="/wiki/Core_data_integration" title="Core data integration">Core data integration</a></li> <li><a href="/wiki/Customer_data_integration" class="mw-redirect" title="Customer data integration">Customer data integration</a></li> <li><a href="/wiki/Cyberinfrastructure" title="Cyberinfrastructure">Cyberinfrastructure</a></li> <li><a href="/wiki/Data_blending" title="Data blending">Data blending</a></li> <li><a href="/wiki/Data_curation" title="Data curation">Data curation</a></li> <li><a href="/wiki/Data_fusion" title="Data fusion">Data fusion</a></li> <li><a href="/wiki/Data_mapping" title="Data mapping">Data mapping</a></li> <li><a href="/wiki/Data_wrangling" title="Data wrangling">Data wrangling</a></li> <li><a href="/wiki/Database_model" title="Database model">Database model</a></li> <li><a href="/wiki/Dataspaces" class="mw-redirect" title="Dataspaces">Dataspaces</a></li> <li><a href="/wiki/Edge_data_integration" title="Edge data integration">Edge data integration</a></li> <li><a href="/wiki/Enterprise_application_integration" title="Enterprise application integration">Enterprise application integration</a></li> <li><a href="/wiki/Enterprise_architecture_framework" title="Enterprise architecture framework">Enterprise architecture framework</a></li> <li><a href="/wiki/Enterprise_information_integration" title="Enterprise information integration">Enterprise information integration</a> (EII)</li> <li><a href="/wiki/Enterprise_integration" title="Enterprise integration">Enterprise integration</a></li> <li>Geodi: Geoscientific Data Integration</li> <li><a href="/wiki/Information_integration" title="Information integration">Information integration</a></li> <li><a href="/wiki/Information_silo" title="Information silo">Information silo</a></li> <li><a href="/wiki/Integration_Competency_Center" class="mw-redirect" title="Integration Competency Center">Integration Competency Center</a></li> <li><a href="/wiki/Integration_Consortium" title="Integration Consortium">Integration Consortium</a></li> <li><a rel="nofollow" class="external text" href="http://15926.org">ISO 15926</a>: Integration of life-cycle data for process plants including oil and gas production facilities</li> <li><a href="/wiki/JXTA" title="JXTA">JXTA</a></li> <li><a href="/wiki/Master_data_management" title="Master data management">Master data management</a></li> <li><a href="/wiki/Object-relational_mapping" class="mw-redirect" title="Object-relational mapping">Object-relational mapping</a></li> <li><a href="/wiki/Open_Text" class="mw-redirect" title="Open Text">Open Text</a></li> <li><a href="/wiki/Semantic_integration" title="Semantic integration">Semantic integration</a></li> <li><a href="/wiki/Schema_matching" title="Schema matching">Schema matching</a></li> <li><a href="/wiki/Three_schema_approach" class="mw-redirect" title="Three schema approach">Three schema approach</a></li> <li><a href="/wiki/UDEF" class="mw-redirect" title="UDEF">UDEF</a></li> <li><a href="/wiki/Web_data_integration" title="Web data integration">Web data integration</a></li> <li><a href="/wiki/Web_service" title="Web service">Web service</a></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Data_integration&action=edit&section=8" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-refone-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-refone_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-refone_1-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-refone_1-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"> <style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output 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