Computing the Clique-Width of Large Path Powers in Linear Time via a New Characterisation of Clique-Width
Identifieur interne : 001B34 ( Istex/Corpus ); précédent : 001B33; suivant : 001B35Computing the Clique-Width of Large Path Powers in Linear Time via a New Characterisation of Clique-Width
Auteurs : Pinar Heggernes ; Daniel Meister ; Udi RoticsSource :
- Lecture Notes in Computer Science [ 0302-9743 ] ; 2011.
Abstract
Abstract: Clique-width is one of the most important graph parameters, as many NP-hard graph problems are solvable in linear time on graphs of bounded clique-width. Unfortunately, the computation of clique-width is among the hardest problems. In fact, we do not know of any other algorithm than brute force for the exact computation of clique-width on any large graph class of unbounded clique-width. Another difficulty about clique-width is the lack of alternative characterisations of it that might help in coping with its hardness. In this paper, we present two results. The first is a new characterisation of clique-width based on rooted binary trees, completely without the use of labelled graphs. Our second result is the exact computation of the clique-width of large path powers in polynomial time, which has been an open problem for a decade. The presented new characterisation is used to achieve this latter result. With our result, large k-path powers constitute the first non-trivial infinite class of graphs of unbounded clique-width whose clique-width can be computed exactly in polynomial time.
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DOI: 10.1007/978-3-642-20712-9_18
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<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">Computing the Clique-Width of Large Path Powers in Linear Time via a New Characterisation of Clique-Width</title><author><name sortKey="Heggernes, Pinar" sort="Heggernes, Pinar" uniqKey="Heggernes P" first="Pinar" last="Heggernes">Pinar Heggernes</name><affiliation><mods:affiliation>Department of Informatics, University of Bergen, Norway</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: pinar.heggernes@ii.uib.no</mods:affiliation></affiliation></author><author><name sortKey="Meister, Daniel" sort="Meister, Daniel" uniqKey="Meister D" first="Daniel" last="Meister">Daniel Meister</name><affiliation><mods:affiliation>Theoretical Computer Science, University of Trier, Germany</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: daniel.meister@uni-trier.de</mods:affiliation></affiliation></author><author><name sortKey="Rotics, Udi" sort="Rotics, Udi" uniqKey="Rotics U" first="Udi" last="Rotics">Udi Rotics</name><affiliation><mods:affiliation>Netanya Academic College, Netanya, Israel</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: rotics@netanya.ac.il</mods:affiliation></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:2295D514E9F8ADB8A3C9A42608FAE803C35104FC</idno><date when="2011" year="2011">2011</date><idno type="doi">10.1007/978-3-642-20712-9_18</idno><idno type="url">https://api.istex.fr/document/2295D514E9F8ADB8A3C9A42608FAE803C35104FC/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">001B34</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">001B34</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Computing the Clique-Width of Large Path Powers in Linear Time via a New Characterisation of Clique-Width</title><author><name sortKey="Heggernes, Pinar" sort="Heggernes, Pinar" uniqKey="Heggernes P" first="Pinar" last="Heggernes">Pinar Heggernes</name><affiliation><mods:affiliation>Department of Informatics, University of Bergen, Norway</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: pinar.heggernes@ii.uib.no</mods:affiliation></affiliation></author><author><name sortKey="Meister, Daniel" sort="Meister, Daniel" uniqKey="Meister D" first="Daniel" last="Meister">Daniel Meister</name><affiliation><mods:affiliation>Theoretical Computer Science, University of Trier, Germany</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: daniel.meister@uni-trier.de</mods:affiliation></affiliation></author><author><name sortKey="Rotics, Udi" sort="Rotics, Udi" uniqKey="Rotics U" first="Udi" last="Rotics">Udi Rotics</name><affiliation><mods:affiliation>Netanya Academic College, Netanya, Israel</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: rotics@netanya.ac.il</mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="s">Lecture Notes in Computer Science</title><imprint><date>2011</date></imprint><idno type="ISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="ISSN">0302-9743</idno></series><idno type="istex">2295D514E9F8ADB8A3C9A42608FAE803C35104FC</idno><idno type="DOI">10.1007/978-3-642-20712-9_18</idno><idno type="ChapterID">18</idno><idno type="ChapterID">Chap18</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0302-9743</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: Clique-width is one of the most important graph parameters, as many NP-hard graph problems are solvable in linear time on graphs of bounded clique-width. Unfortunately, the computation of clique-width is among the hardest problems. In fact, we do not know of any other algorithm than brute force for the exact computation of clique-width on any large graph class of unbounded clique-width. Another difficulty about clique-width is the lack of alternative characterisations of it that might help in coping with its hardness. In this paper, we present two results. The first is a new characterisation of clique-width based on rooted binary trees, completely without the use of labelled graphs. Our second result is the exact computation of the clique-width of large path powers in polynomial time, which has been an open problem for a decade. The presented new characterisation is used to achieve this latter result. With our result, large k-path powers constitute the first non-trivial infinite class of graphs of unbounded clique-width whose clique-width can be computed exactly in polynomial time.</div></front></TEI><istex><corpusName>springer</corpusName><author><json:item><name>Pinar Heggernes</name><affiliations><json:string>Department of Informatics, University of Bergen, Norway</json:string><json:string>E-mail: pinar.heggernes@ii.uib.no</json:string></affiliations></json:item><json:item><name>Daniel Meister</name><affiliations><json:string>Theoretical Computer Science, University of Trier, Germany</json:string><json:string>E-mail: daniel.meister@uni-trier.de</json:string></affiliations></json:item><json:item><name>Udi Rotics</name><affiliations><json:string>Netanya Academic College, Netanya, Israel</json:string><json:string>E-mail: rotics@netanya.ac.il</json:string></affiliations></json:item></author><language><json:string>eng</json:string></language><originalGenre><json:string>OriginalPaper</json:string></originalGenre><abstract>Abstract: Clique-width is one of the most important graph parameters, as many NP-hard graph problems are solvable in linear time on graphs of bounded clique-width. Unfortunately, the computation of clique-width is among the hardest problems. In fact, we do not know of any other algorithm than brute force for the exact computation of clique-width on any large graph class of unbounded clique-width. Another difficulty about clique-width is the lack of alternative characterisations of it that might help in coping with its hardness. In this paper, we present two results. The first is a new characterisation of clique-width based on rooted binary trees, completely without the use of labelled graphs. Our second result is the exact computation of the clique-width of large path powers in polynomial time, which has been an open problem for a decade. The presented new characterisation is used to achieve this latter result. With our result, large k-path powers constitute the first non-trivial infinite class of graphs of unbounded clique-width whose clique-width can be computed exactly in polynomial time.</abstract><qualityIndicators><score>8.564</score><pdfVersion>1.6</pdfVersion><pdfPageSize>429.442 x 659.895 pts</pdfPageSize><refBibsNative>false</refBibsNative><keywordCount>0</keywordCount><abstractCharCount>1108</abstractCharCount><pdfWordCount>8213</pdfWordCount><pdfCharCount>33532</pdfCharCount><pdfPageCount>14</pdfPageCount><abstractWordCount>172</abstractWordCount></qualityIndicators><title>Computing the Clique-Width of Large Path Powers in Linear Time via a New Characterisation of Clique-Width</title><chapterId><json:string>18</json:string><json:string>Chap18</json:string></chapterId><refBibs><json:item><author><json:item><name>H Bodlaender</name></json:item></author><host><volume>25</volume><pages><last>1317</last><first>1305</first></pages><author></author><title>SIAM Journal on Computing</title><publicationDate>1996</publicationDate></host><title>A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth</title><publicationDate>1996</publicationDate></json:item><json:item><author><json:item><name>A Brandstädt</name></json:item><json:item><name>F Dragan</name></json:item><json:item><name>H.-O Le</name></json:item><json:item><name>R Mosca</name></json:item></author><host><pages><last>645</last><first>623</first></pages><author></author><title>New Graph Classes of Bounded Clique-Width. 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UK</json:string></affiliations></json:item><json:item><name>Jon M. Kleinberg</name><affiliations><json:string>Cornell University, Ithaca, NY, USA</json:string></affiliations></json:item><json:item><name>Friedemann Mattern</name><affiliations><json:string>ETH Zurich, Zurich, Switzerland</json:string></affiliations></json:item><json:item><name>John C. Mitchell</name><affiliations><json:string>Stanford University, Stanford, CA, USA</json:string></affiliations></json:item><json:item><name>Moni Naor</name><affiliations><json:string>Weizmann Institute of Science, Rehovot, Israel</json:string></affiliations></json:item><json:item><name>Oscar Nierstrasz</name><affiliations><json:string>University of Bern, Bern, Switzerland</json:string></affiliations></json:item><json:item><name>C. Pandu Rangan</name><affiliations><json:string>Indian Institute of Technology, Madras, India</json:string></affiliations></json:item><json:item><name>Bernhard Steffen</name><affiliations><json:string>University of Dortmund, Dortmund, Germany</json:string></affiliations></json:item><json:item><name>Madhu Sudan</name><affiliations><json:string>Massachusetts Institute of Technology, MA, USA</json:string></affiliations></json:item><json:item><name>Demetri Terzopoulos</name><affiliations><json:string>University of California, Los Angeles, CA, USA</json:string></affiliations></json:item><json:item><name>Doug Tygar</name><affiliations><json:string>University of California, Berkeley, CA, USA</json:string></affiliations></json:item><json:item><name>Moshe Y. Vardi</name><affiliations><json:string>Rice University, Houston, TX, USA</json:string></affiliations></json:item><json:item><name>Gerhard Weikum</name><affiliations><json:string>Max-Planck Institute of Computer Science, Saarbrücken, Germany</json:string></affiliations></json:item></editor><issn><json:string>0302-9743</json:string></issn><language><json:string>unknown</json:string></language><eissn><json:string>1611-3349</json:string></eissn><title>Lecture Notes in Computer Science</title><copyrightDate>2011</copyrightDate></serie><host><editor><json:item><name>Alexander Kulikov</name><affiliations><json:string>Steklov Institute of Mathematics at St. Petersburg, 27 Fontanka, 191023, St.Petersburg, Russia</json:string><json:string>E-mail: kulikov@logic.pdmi.ras.ru</json:string></affiliations></json:item><json:item><name>Nikolay Vereshchagin</name><affiliations><json:string>Department of Mathematical Logic and Theory of Algorithms, Moscow State University, Leninskie gory, 119991, Moscow, Russia</json:string><json:string>E-mail: nikolay.vereshchagin@gmail.com</json:string></affiliations></json:item></editor><subject><json:item><value>Computer Science</value></json:item><json:item><value>Computer Science</value></json:item><json:item><value>Algorithm Analysis and Problem Complexity</value></json:item><json:item><value>Logics and Meanings of Programs</value></json:item><json:item><value>Mathematical Logic and Formal Languages</value></json:item><json:item><value>Discrete Mathematics in Computer Science</value></json:item><json:item><value>Computation by Abstract Devices</value></json:item><json:item><value>Mathematics of Computing</value></json:item></subject><isbn><json:string>978-3-642-20711-2</json:string></isbn><language><json:string>unknown</json:string></language><eissn><json:string>1611-3349</json:string></eissn><title>Computer Science – Theory and Applications</title><bookId><json:string>978-3-642-20712-9</json:string></bookId><volume>6651</volume><pages><last>246</last><first>233</first></pages><issn><json:string>0302-9743</json:string></issn><genre><json:string>book-series</json:string></genre><eisbn><json:string>978-3-642-20712-9</json:string></eisbn><copyrightDate>2011</copyrightDate><doi><json:string>10.1007/978-3-642-20712-9</json:string></doi></host><publicationDate>2011</publicationDate><copyrightDate>2011</copyrightDate><doi><json:string>10.1007/978-3-642-20712-9_18</json:string></doi><id>2295D514E9F8ADB8A3C9A42608FAE803C35104FC</id><score>0.60804784</score><fulltext><json:item><extension>pdf</extension><original>true</original><mimetype>application/pdf</mimetype><uri>https://api.istex.fr/document/2295D514E9F8ADB8A3C9A42608FAE803C35104FC/fulltext/pdf</uri></json:item><json:item><extension>zip</extension><original>false</original><mimetype>application/zip</mimetype><uri>https://api.istex.fr/document/2295D514E9F8ADB8A3C9A42608FAE803C35104FC/fulltext/zip</uri></json:item><istex:fulltextTEI uri="https://api.istex.fr/document/2295D514E9F8ADB8A3C9A42608FAE803C35104FC/fulltext/tei"><teiHeader><fileDesc><titleStmt><title level="a" type="main" xml:lang="en">Computing the Clique-Width of Large Path Powers in Linear Time via a New Characterisation of Clique-Width</title><respStmt><resp>Références bibliographiques récupérées via GROBID</resp><name resp="ISTEX-API">ISTEX-API (INIST-CNRS)</name></respStmt><respStmt><resp>Références bibliographiques récupérées via GROBID</resp><name resp="ISTEX-API">ISTEX-API (INIST-CNRS)</name></respStmt></titleStmt><publicationStmt><authority>ISTEX</authority><publisher>Springer Berlin Heidelberg</publisher><pubPlace>Berlin, Heidelberg</pubPlace><availability><p>Springer Berlin Heidelberg, 2011</p></availability><date>2011</date></publicationStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a" type="main" xml:lang="en">Computing the Clique-Width of Large Path Powers in Linear Time via a New Characterisation of Clique-Width</title><author xml:id="author-1"><persName><forename type="first">Pinar</forename><surname>Heggernes</surname></persName><email>pinar.heggernes@ii.uib.no</email><affiliation>Department of Informatics, University of Bergen, Norway</affiliation></author><author xml:id="author-2"><persName><forename type="first">Daniel</forename><surname>Meister</surname></persName><email>daniel.meister@uni-trier.de</email><affiliation>Theoretical Computer Science, University of Trier, Germany</affiliation></author><author xml:id="author-3"><persName><forename type="first">Udi</forename><surname>Rotics</surname></persName><email>rotics@netanya.ac.il</email><affiliation>Netanya Academic College, Netanya, Israel</affiliation></author></analytic><monogr><title level="m">Computer Science – Theory and Applications</title><title level="m" type="sub">6th International Computer Science Symposium in Russia, CSR 2011, St. Petersburg, Russia, June 14-18, 2011. Proceedings</title><idno type="pISBN">978-3-642-20711-2</idno><idno type="eISBN">978-3-642-20712-9</idno><idno type="pISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="DOI">10.1007/978-3-642-20712-9</idno><idno type="book-ID">978-3-642-20712-9</idno><idno type="book-title-ID">270039</idno><idno type="book-sequence-number">6651</idno><idno type="book-volume-number">6651</idno><idno type="book-chapter-count">36</idno><editor><persName><forename type="first">Alexander</forename><surname>Kulikov</surname></persName><email>kulikov@logic.pdmi.ras.ru</email><affiliation>Steklov Institute of Mathematics at St. Petersburg, 27 Fontanka, 191023, St.Petersburg, Russia</affiliation></editor><editor><persName><forename type="first">Nikolay</forename><surname>Vereshchagin</surname></persName><email>nikolay.vereshchagin@gmail.com</email><affiliation>Department of Mathematical Logic and Theory of Algorithms, Moscow State University, Leninskie gory, 119991, Moscow, Russia</affiliation></editor><imprint><publisher>Springer Berlin Heidelberg</publisher><pubPlace>Berlin, Heidelberg</pubPlace><date type="published" when="2011"></date><biblScope unit="volume">6651</biblScope><biblScope unit="page" from="233">233</biblScope><biblScope unit="page" to="246">246</biblScope></imprint></monogr><series><title level="s">Lecture Notes in Computer Science</title><editor><persName><forename type="first">David</forename><surname>Hutchison</surname></persName><affiliation>Lancaster University, Lancaster, UK</affiliation></editor><editor><persName><forename type="first">Takeo</forename><surname>Kanade</surname></persName><affiliation>Carnegie Mellon University, Pittsburgh, PA, USA</affiliation></editor><editor><persName><forename type="first">Josef</forename><surname>Kittler</surname></persName><affiliation>University of Surrey, Guildford, UK</affiliation></editor><editor><persName><forename type="first">Jon</forename><forename type="first">M.</forename><surname>Kleinberg</surname></persName><affiliation>Cornell University, Ithaca, NY, USA</affiliation></editor><editor><persName><forename type="first">Friedemann</forename><surname>Mattern</surname></persName><affiliation>ETH Zurich, Zurich, Switzerland</affiliation></editor><editor><persName><forename type="first">John</forename><forename type="first">C.</forename><surname>Mitchell</surname></persName><affiliation>Stanford University, Stanford, CA, USA</affiliation></editor><editor><persName><forename type="first">Moni</forename><surname>Naor</surname></persName><affiliation>Weizmann Institute of Science, Rehovot, Israel</affiliation></editor><editor><persName><forename type="first">Oscar</forename><surname>Nierstrasz</surname></persName><affiliation>University of Bern, Bern, Switzerland</affiliation></editor><editor><persName><forename type="first">C.</forename><surname>Pandu Rangan</surname></persName><affiliation>Indian Institute of Technology, Madras, India</affiliation></editor><editor><persName><forename type="first">Bernhard</forename><surname>Steffen</surname></persName><affiliation>University of Dortmund, Dortmund, Germany</affiliation></editor><editor><persName><forename type="first">Madhu</forename><surname>Sudan</surname></persName><affiliation>Massachusetts Institute of Technology, MA, USA</affiliation></editor><editor><persName><forename type="first">Demetri</forename><surname>Terzopoulos</surname></persName><affiliation>University of California, Los Angeles, CA, USA</affiliation></editor><editor><persName><forename type="first">Doug</forename><surname>Tygar</surname></persName><affiliation>University of California, Berkeley, CA, USA</affiliation></editor><editor><persName><forename type="first">Moshe</forename><forename type="first">Y.</forename><surname>Vardi</surname></persName><affiliation>Rice University, Houston, TX, USA</affiliation></editor><editor><persName><forename type="first">Gerhard</forename><surname>Weikum</surname></persName><affiliation>Max-Planck Institute of Computer Science, Saarbrücken, Germany</affiliation></editor><biblScope><date>2011</date></biblScope><idno type="pISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="series-Id">558</idno></series><idno type="istex">2295D514E9F8ADB8A3C9A42608FAE803C35104FC</idno><idno type="DOI">10.1007/978-3-642-20712-9_18</idno><idno type="ChapterID">18</idno><idno type="ChapterID">Chap18</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>2011</date></creation><langUsage><language ident="en">en</language></langUsage><abstract xml:lang="en"><p>Abstract: Clique-width is one of the most important graph parameters, as many NP-hard graph problems are solvable in linear time on graphs of bounded clique-width. Unfortunately, the computation of clique-width is among the hardest problems. In fact, we do not know of any other algorithm than brute force for the exact computation of clique-width on any large graph class of unbounded clique-width. Another difficulty about clique-width is the lack of alternative characterisations of it that might help in coping with its hardness. In this paper, we present two results. The first is a new characterisation of clique-width based on rooted binary trees, completely without the use of labelled graphs. Our second result is the exact computation of the clique-width of large path powers in polynomial time, which has been an open problem for a decade. The presented new characterisation is used to achieve this latter result. With our result, large k-path powers constitute the first non-trivial infinite class of graphs of unbounded clique-width whose clique-width can be computed exactly in polynomial time.</p></abstract><textClass><keywords scheme="Book-Subject-Collection"><list><label>SUCO11645</label><item><term>Computer Science</term></item></list></keywords></textClass><textClass><keywords scheme="Book-Subject-Group"><list><label>I</label><label>I16021</label><label>I1603X</label><label>I16048</label><label>I17028</label><label>I16013</label><label>I17001</label><item><term>Computer Science</term></item><item><term>Algorithm Analysis and Problem Complexity</term></item><item><term>Logics and Meanings of Programs</term></item><item><term>Mathematical Logic and Formal Languages</term></item><item><term>Discrete Mathematics in Computer Science</term></item><item><term>Computation by Abstract Devices</term></item><item><term>Mathematics of 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California</OrgName><OrgAddress><City>Berkeley</City><State>CA</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff14"><OrgName>Rice University</OrgName><OrgAddress><City>Houston</City><State>TX</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff15"><OrgName>Max-Planck Institute of Computer Science</OrgName><OrgAddress><City>Saarbrücken</City><Country>Germany</Country></OrgAddress></Affiliation></EditorGroup></SeriesHeader><Book Language="En"><BookInfo BookProductType="Proceedings" ContainsESM="No" Language="En" MediaType="eBook" NumberingDepth="2" NumberingStyle="ContentOnly" OutputMedium="All" TocLevels="0"><BookID>978-3-642-20712-9</BookID><BookTitle>Computer Science – Theory and Applications</BookTitle><BookSubTitle>6th International Computer Science Symposium in Russia, CSR 2011, St. Petersburg, Russia, June 14-18, 2011. Proceedings</BookSubTitle><BookVolumeNumber>6651</BookVolumeNumber><BookSequenceNumber>6651</BookSequenceNumber><BookDOI>10.1007/978-3-642-20712-9</BookDOI><BookTitleID>270039</BookTitleID><BookPrintISBN>978-3-642-20711-2</BookPrintISBN><BookElectronicISBN>978-3-642-20712-9</BookElectronicISBN><BookChapterCount>36</BookChapterCount><BookCopyright><CopyrightHolderName>Springer Berlin Heidelberg</CopyrightHolderName><CopyrightYear>2011</CopyrightYear></BookCopyright><BookSubjectGroup><BookSubject Code="I" Type="Primary">Computer Science</BookSubject><BookSubject Code="I16021" Priority="1" Type="Secondary">Algorithm Analysis and Problem Complexity</BookSubject><BookSubject Code="I1603X" Priority="2" Type="Secondary">Logics and Meanings of Programs</BookSubject><BookSubject Code="I16048" Priority="3" Type="Secondary">Mathematical Logic and Formal Languages</BookSubject><BookSubject Code="I17028" Priority="4" Type="Secondary">Discrete Mathematics in Computer Science</BookSubject><BookSubject Code="I16013" Priority="5" Type="Secondary">Computation by Abstract Devices</BookSubject><BookSubject Code="I17001" Priority="6" Type="Secondary">Mathematics of Computing</BookSubject><SubjectCollection Code="SUCO11645">Computer Science</SubjectCollection></BookSubjectGroup><BookContext><SeriesID>558</SeriesID></BookContext></BookInfo><BookHeader><EditorGroup><Editor AffiliationIDS="Aff16"><EditorName DisplayOrder="Western"><GivenName>Alexander</GivenName><FamilyName>Kulikov</FamilyName></EditorName><Contact><Email>kulikov@logic.pdmi.ras.ru</Email></Contact></Editor><Editor AffiliationIDS="Aff17"><EditorName DisplayOrder="Western"><GivenName>Nikolay</GivenName><FamilyName>Vereshchagin</FamilyName></EditorName><Contact><Email>nikolay.vereshchagin@gmail.com</Email></Contact></Editor><Affiliation ID="Aff16"><OrgName>Steklov Institute of Mathematics at St. Petersburg</OrgName><OrgAddress><Street>27 Fontanka</Street><Postcode>191023</Postcode><City>St.Petersburg</City><Country>Russia</Country></OrgAddress></Affiliation><Affiliation ID="Aff17"><OrgDivision>Department of Mathematical Logic and Theory of Algorithms</OrgDivision><OrgName>Moscow State University</OrgName><OrgAddress><Street>Leninskie gory</Street><Postcode>119991</Postcode><City>Moscow</City><Country>Russia</Country></OrgAddress></Affiliation></EditorGroup></BookHeader><Chapter ID="Chap18" Language="En"><ChapterInfo ChapterType="OriginalPaper" ContainsESM="No" NumberingDepth="2" NumberingStyle="ContentOnly" TocLevels="0"><ChapterID>18</ChapterID><ChapterDOI>10.1007/978-3-642-20712-9_18</ChapterDOI><ChapterSequenceNumber>18</ChapterSequenceNumber><ChapterTitle Language="En">Computing the Clique-Width of Large Path Powers in Linear Time via a New Characterisation of Clique-Width</ChapterTitle><ChapterFirstPage>233</ChapterFirstPage><ChapterLastPage>246</ChapterLastPage><ChapterCopyright><CopyrightHolderName>Springer-Verlag Berlin Heidelberg</CopyrightHolderName><CopyrightYear>2011</CopyrightYear></ChapterCopyright><ChapterGrants Type="Regular"><MetadataGrant Grant="OpenAccess"></MetadataGrant><AbstractGrant Grant="OpenAccess"></AbstractGrant><BodyPDFGrant Grant="Restricted"></BodyPDFGrant><BodyHTMLGrant Grant="Restricted"></BodyHTMLGrant><BibliographyGrant Grant="Restricted"></BibliographyGrant><ESMGrant Grant="Restricted"></ESMGrant></ChapterGrants><ChapterContext><SeriesID>558</SeriesID><BookID>978-3-642-20712-9</BookID><BookTitle>Computer Science – Theory and Applications</BookTitle></ChapterContext></ChapterInfo><ChapterHeader><AuthorGroup><Author AffiliationIDS="Aff18"><AuthorName DisplayOrder="Western"><GivenName>Pinar</GivenName><FamilyName>Heggernes</FamilyName></AuthorName><Contact><Email>pinar.heggernes@ii.uib.no</Email></Contact></Author><Author AffiliationIDS="Aff19"><AuthorName DisplayOrder="Western"><GivenName>Daniel</GivenName><FamilyName>Meister</FamilyName></AuthorName><Contact><Email>daniel.meister@uni-trier.de</Email></Contact></Author><Author AffiliationIDS="Aff20"><AuthorName DisplayOrder="Western"><GivenName>Udi</GivenName><FamilyName>Rotics</FamilyName></AuthorName><Contact><Email>rotics@netanya.ac.il</Email></Contact></Author><Affiliation ID="Aff18"><OrgDivision>Department of Informatics</OrgDivision><OrgName>University of Bergen</OrgName><OrgAddress><Country>Norway</Country></OrgAddress></Affiliation><Affiliation ID="Aff19"><OrgDivision>Theoretical Computer Science</OrgDivision><OrgName>University of Trier</OrgName><OrgAddress><Country>Germany</Country></OrgAddress></Affiliation><Affiliation ID="Aff20"><OrgName>Netanya Academic College</OrgName><OrgAddress><City>Netanya</City><Country>Israel</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>Clique-width is one of the most important graph parameters, as many NP-hard graph problems are solvable in linear time on graphs of bounded clique-width. Unfortunately, the computation of clique-width is among the hardest problems. In fact, we do not know of any other algorithm than brute force for the exact computation of clique-width on any large graph class of unbounded clique-width. Another difficulty about clique-width is the lack of alternative characterisations of it that might help in coping with its hardness. In this paper, we present two results. The first is a new characterisation of clique-width based on rooted binary trees, completely without the use of labelled graphs. Our second result is the exact computation of the clique-width of large path powers in polynomial time, which has been an open problem for a decade. The presented new characterisation is used to achieve this latter result. With our result, large <Emphasis Type="Italic">k</Emphasis>-path powers constitute the first non-trivial infinite class of graphs of unbounded clique-width whose clique-width can be computed exactly in polynomial time.</Para></Abstract></ChapterHeader><NoBody></NoBody></Chapter></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Computing the Clique-Width of Large Path Powers in Linear Time via a New Characterisation of Clique-Width</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Computing the Clique-Width of Large Path Powers in Linear Time via a New Characterisation of Clique-Width</title></titleInfo><name type="personal"><namePart type="given">Pinar</namePart><namePart type="family">Heggernes</namePart><affiliation>Department of Informatics, University of Bergen, Norway</affiliation><affiliation>E-mail: pinar.heggernes@ii.uib.no</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Daniel</namePart><namePart type="family">Meister</namePart><affiliation>Theoretical Computer Science, University of Trier, Germany</affiliation><affiliation>E-mail: daniel.meister@uni-trier.de</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Udi</namePart><namePart type="family">Rotics</namePart><affiliation>Netanya Academic College, Netanya, Israel</affiliation><affiliation>E-mail: rotics@netanya.ac.il</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="conference" displayLabel="OriginalPaper"></genre><originInfo><publisher>Springer Berlin Heidelberg</publisher><place><placeTerm type="text">Berlin, Heidelberg</placeTerm></place><dateIssued encoding="w3cdtf">2011</dateIssued><copyrightDate encoding="w3cdtf">2011</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType></physicalDescription><abstract lang="en">Abstract: Clique-width is one of the most important graph parameters, as many NP-hard graph problems are solvable in linear time on graphs of bounded clique-width. Unfortunately, the computation of clique-width is among the hardest problems. In fact, we do not know of any other algorithm than brute force for the exact computation of clique-width on any large graph class of unbounded clique-width. Another difficulty about clique-width is the lack of alternative characterisations of it that might help in coping with its hardness. In this paper, we present two results. The first is a new characterisation of clique-width based on rooted binary trees, completely without the use of labelled graphs. Our second result is the exact computation of the clique-width of large path powers in polynomial time, which has been an open problem for a decade. The presented new characterisation is used to achieve this latter result. With our result, large k-path powers constitute the first non-trivial infinite class of graphs of unbounded clique-width whose clique-width can be computed exactly in polynomial time.</abstract><relatedItem type="host"><titleInfo><title>Computer Science – Theory and Applications</title><subTitle>6th International Computer Science Symposium in Russia, CSR 2011, St. Petersburg, Russia, June 14-18, 2011. Proceedings</subTitle></titleInfo><name type="personal"><namePart type="given">Alexander</namePart><namePart type="family">Kulikov</namePart><affiliation>Steklov Institute of Mathematics at St. Petersburg, 27 Fontanka, 191023, St.Petersburg, Russia</affiliation><affiliation>E-mail: kulikov@logic.pdmi.ras.ru</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Nikolay</namePart><namePart type="family">Vereshchagin</namePart><affiliation>Department of Mathematical Logic and Theory of Algorithms, Moscow State University, Leninskie gory, 119991, Moscow, Russia</affiliation><affiliation>E-mail: nikolay.vereshchagin@gmail.com</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><genre type="book-series" displayLabel="Proceedings"></genre><originInfo><copyrightDate encoding="w3cdtf">2011</copyrightDate><issuance>monographic</issuance></originInfo><subject><genre>Book-Subject-Collection</genre><topic authority="SpringerSubjectCodes" authorityURI="SUCO11645">Computer Science</topic></subject><subject><genre>Book-Subject-Group</genre><topic authority="SpringerSubjectCodes" authorityURI="I">Computer Science</topic><topic authority="SpringerSubjectCodes" authorityURI="I16021">Algorithm Analysis and Problem Complexity</topic><topic authority="SpringerSubjectCodes" authorityURI="I1603X">Logics and Meanings of Programs</topic><topic authority="SpringerSubjectCodes" authorityURI="I16048">Mathematical Logic and Formal Languages</topic><topic authority="SpringerSubjectCodes" authorityURI="I17028">Discrete Mathematics in Computer Science</topic><topic authority="SpringerSubjectCodes" authorityURI="I16013">Computation by Abstract Devices</topic><topic authority="SpringerSubjectCodes" authorityURI="I17001">Mathematics of Computing</topic></subject><identifier type="DOI">10.1007/978-3-642-20712-9</identifier><identifier type="ISBN">978-3-642-20711-2</identifier><identifier type="eISBN">978-3-642-20712-9</identifier><identifier type="ISSN">0302-9743</identifier><identifier type="eISSN">1611-3349</identifier><identifier type="BookTitleID">270039</identifier><identifier type="BookID">978-3-642-20712-9</identifier><identifier type="BookChapterCount">36</identifier><identifier type="BookVolumeNumber">6651</identifier><identifier type="BookSequenceNumber">6651</identifier><part><date>2011</date><detail type="volume"><number>6651</number><caption>vol.</caption></detail><extent unit="pages"><start>233</start><end>246</end></extent></part><recordInfo><recordOrigin>Springer Berlin Heidelberg, 2011</recordOrigin></recordInfo></relatedItem><relatedItem type="series"><titleInfo><title>Lecture Notes in Computer Science</title></titleInfo><name type="personal"><namePart type="given">David</namePart><namePart type="family">Hutchison</namePart><affiliation>Lancaster University, Lancaster, UK</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Takeo</namePart><namePart type="family">Kanade</namePart><affiliation>Carnegie Mellon University, Pittsburgh, PA, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Josef</namePart><namePart type="family">Kittler</namePart><affiliation>University of Surrey, Guildford, UK</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Jon</namePart><namePart type="given">M.</namePart><namePart type="family">Kleinberg</namePart><affiliation>Cornell University, Ithaca, NY, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Friedemann</namePart><namePart type="family">Mattern</namePart><affiliation>ETH Zurich, Zurich, Switzerland</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">John</namePart><namePart type="given">C.</namePart><namePart type="family">Mitchell</namePart><affiliation>Stanford University, Stanford, CA, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Moni</namePart><namePart type="family">Naor</namePart><affiliation>Weizmann Institute of Science, Rehovot, Israel</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Oscar</namePart><namePart type="family">Nierstrasz</namePart><affiliation>University of Bern, Bern, Switzerland</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">C.</namePart><namePart type="family">Pandu Rangan</namePart><affiliation>Indian Institute of Technology, Madras, India</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Bernhard</namePart><namePart type="family">Steffen</namePart><affiliation>University of Dortmund, Dortmund, Germany</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Madhu</namePart><namePart type="family">Sudan</namePart><affiliation>Massachusetts Institute of Technology, MA, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Demetri</namePart><namePart type="family">Terzopoulos</namePart><affiliation>University of California, Los Angeles, CA, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Doug</namePart><namePart type="family">Tygar</namePart><affiliation>University of California, Berkeley, CA, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Moshe</namePart><namePart type="given">Y.</namePart><namePart type="family">Vardi</namePart><affiliation>Rice University, Houston, TX, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Gerhard</namePart><namePart type="family">Weikum</namePart><affiliation>Max-Planck Institute of Computer Science, Saarbrücken, Germany</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><originInfo><copyrightDate encoding="w3cdtf">2011</copyrightDate><issuance>serial</issuance></originInfo><identifier type="ISSN">0302-9743</identifier><identifier type="eISSN">1611-3349</identifier><identifier type="SeriesID">558</identifier><recordInfo><recordOrigin>Springer Berlin Heidelberg, 2011</recordOrigin></recordInfo></relatedItem><identifier type="istex">2295D514E9F8ADB8A3C9A42608FAE803C35104FC</identifier><identifier type="DOI">10.1007/978-3-642-20712-9_18</identifier><identifier type="ChapterID">18</identifier><identifier type="ChapterID">Chap18</identifier><accessCondition type="use and reproduction" contentType="copyright">Springer Berlin Heidelberg, 2011</accessCondition><recordInfo><recordContentSource>SPRINGER</recordContentSource><recordOrigin>Springer-Verlag Berlin Heidelberg, 2011</recordOrigin></recordInfo></mods></metadata></istex></record>Pour manipuler ce document sous Unix (Dilib)
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