A SAT Based Effective Algorithm for the Directed Hamiltonian Cycle Problem
Identifieur interne : 003860 ( Istex/Corpus ); précédent : 003859; suivant : 003861A SAT Based Effective Algorithm for the Directed Hamiltonian Cycle Problem
Auteurs : Gerold J Ger ; Weixiong ZhangSource :
- Lecture Notes in Computer Science [ 0302-9743 ]
Abstract
Abstract: The Hamiltonian cycle problem (HCP) is an important combinatorial problem with applications in many areas. While thorough theoretical and experimental analyses have been made on the HCP in undirected graphs, little is known for the HCP in directed graphs (DHCP). The contribution of this work is an effective algorithm for the DHCP. Our algorithm explores and exploits the close relationship between the DHCP and the Assignment Problem (AP) and utilizes a technique based on Boolean satisfiability (SAT). By combining effective algorithms for the AP and SAT, our algorithm significantly outperforms previous exact DHCP algorithms including an algorithm based on the award-winning Concorde TSP algorithm.
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DOI: 10.1007/978-3-642-13182-0_20
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While thorough theoretical and experimental analyses have been made on the HCP in undirected graphs, little is known for the HCP in directed graphs (DHCP). The contribution of this work is an effective algorithm for the DHCP. Our algorithm explores and exploits the close relationship between the DHCP and the Assignment Problem (AP) and utilizes a technique based on Boolean satisfiability (SAT). 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While thorough theoretical and experimental analyses have been made on the HCP in undirected graphs, little is known for the HCP in directed graphs (DHCP). The contribution of this work is an effective algorithm for the DHCP. Our algorithm explores and exploits the close relationship between the DHCP and the Assignment Problem (AP) and utilizes a technique based on Boolean satisfiability (SAT). By combining effective algorithms for the AP and SAT, our algorithm significantly outperforms previous exact DHCP algorithms including an algorithm based on the award-winning Concorde TSP algorithm.</p></abstract><textClass ana="subject"><keywords scheme="book-subject-collection"><list><label>SUCO11645</label><item><term>Computer Science</term></item></list></keywords></textClass><textClass ana="subject"><keywords scheme="book-subject"><list><label>I</label><item><term type="Primary">Computer Science</term></item><label>I16021</label><item><term type="Secondary" subtype="priority-1">Algorithm Analysis and Problem Complexity</term></item><label>I1603X</label><item><term type="Secondary" subtype="priority-2">Logics and Meanings of Programs</term></item><label>I16048</label><item><term type="Secondary" subtype="priority-3">Mathematical Logic and Formal Languages</term></item><label>I17028</label><item><term type="Secondary" subtype="priority-4">Discrete Mathematics in Computer 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Science</OrgName><OrgAddress><City>Rehovot</City><Country>Israel</Country></OrgAddress></Affiliation><Affiliation ID="Aff8"><OrgName>University of Bern</OrgName><OrgAddress><City>Bern</City><Country>Switzerland</Country></OrgAddress></Affiliation><Affiliation ID="Aff9"><OrgName>Indian Institute of Technology</OrgName><OrgAddress><City>Madras</City><Country>India</Country></OrgAddress></Affiliation><Affiliation ID="Aff10"><OrgName>University of Dortmund</OrgName><OrgAddress><City>Dortmund</City><Country>Germany</Country></OrgAddress></Affiliation><Affiliation ID="Aff11"><OrgName>Massachusetts Institute of Technology</OrgName><OrgAddress><State>MA</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff12"><OrgName>University of California</OrgName><OrgAddress><City>Los Angeles</City><State>CA</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff13"><OrgName>University of 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>978-3-642-13182-0</BookID><BookTitle>Computer Science – Theory and Applications</BookTitle><BookSubTitle>5th International Computer Science Symposium in Russia, CSR 2010, Kazan, Russia, June 16-20, 2010. Proceedings</BookSubTitle><BookVolumeNumber>6072</BookVolumeNumber><BookSequenceNumber>6072</BookSequenceNumber><BookDOI>10.1007/978-3-642-13182-0</BookDOI><BookTitleID>211548</BookTitleID><BookPrintISBN>978-3-642-13181-3</BookPrintISBN><BookElectronicISBN>978-3-642-13182-0</BookElectronicISBN><BookChapterCount>38</BookChapterCount><BookCopyright><CopyrightHolderName>Springer-Verlag Berlin Heidelberg</CopyrightHolderName><CopyrightYear>2010</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>Farid</GivenName><FamilyName>Ablayev</FamilyName></EditorName><Contact><Email>ablayev@ksu.ru</Email></Contact></Editor><Editor AffiliationIDS="Aff17"><EditorName DisplayOrder="Western"><GivenName>Ernst</GivenName><GivenName>W.</GivenName><FamilyName>Mayr</FamilyName></EditorName><Contact><Email>mayr@in.tum.de</Email></Contact></Editor><Affiliation ID="Aff16"><OrgDivision>Dept. of Theoretical Cybernetics</OrgDivision><OrgName>Kazan State University</OrgName><OrgAddress><Postcode>420008</Postcode><City>Kazan</City><Country>Russia</Country></OrgAddress></Affiliation><Affiliation ID="Aff17"><OrgDivision>Institut für Informatik</OrgDivision><OrgName>Technische Universität München</OrgName><OrgAddress><Postcode>85748</Postcode><City>Garching</City><Country>Germany</Country></OrgAddress></Affiliation></EditorGroup></BookHeader><Chapter ID="Chap20" Language="En"><ChapterInfo ChapterType="OriginalPaper" ContainsESM="No" NumberingDepth="2" NumberingStyle="ContentOnly" TocLevels="0"><ChapterID>20</ChapterID><ChapterDOI>10.1007/978-3-642-13182-0_20</ChapterDOI><ChapterSequenceNumber>20</ChapterSequenceNumber><ChapterTitle Language="En">A SAT Based Effective Algorithm for the Directed Hamiltonian Cycle Problem</ChapterTitle><ChapterFirstPage>216</ChapterFirstPage><ChapterLastPage>227</ChapterLastPage><ChapterCopyright><CopyrightHolderName>Springer-Verlag Berlin Heidelberg</CopyrightHolderName><CopyrightYear>2010</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>978-3-642-13182-0</BookID><BookTitle>Computer Science – Theory and Applications</BookTitle></ChapterContext></ChapterInfo><ChapterHeader><AuthorGroup><Author AffiliationIDS="Aff18"><AuthorName DisplayOrder="Western"><GivenName>Gerold</GivenName><FamilyName>Jäger</FamilyName></AuthorName><Contact><Email>gej@informatik.uni-kiel.de</Email></Contact></Author><Author AffiliationIDS="Aff19"><AuthorName DisplayOrder="Western"><GivenName>Weixiong</GivenName><FamilyName>Zhang</FamilyName></AuthorName><Contact><Email>weixiong.zhang@wustl.edu</Email></Contact></Author><Affiliation ID="Aff18"><OrgDivision>Computer Science Institute</OrgDivision><OrgName>Christian-Albrechts-University of Kiel</OrgName><OrgAddress><Postcode>D-24118</Postcode><City>Kiel</City><Country>Germany</Country></OrgAddress></Affiliation><Affiliation ID="Aff19"><OrgDivision>Department of Computer Science/Department of Genetics</OrgDivision><OrgName>Washington University</OrgName><OrgAddress><City>St. Louis</City><State>Missouri</State><Postcode>63130-4899</Postcode><Country>United States</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>The Hamiltonian cycle problem (HCP) is an important combinatorial problem with applications in many areas. While thorough theoretical and experimental analyses have been made on the HCP in undirected graphs, little is known for the HCP in directed graphs (DHCP). The contribution of this work is an effective algorithm for the DHCP. Our algorithm explores and exploits the close relationship between the DHCP and the Assignment Problem (AP) and utilizes a technique based on Boolean satisfiability (SAT). By combining effective algorithms for the AP and SAT, our algorithm significantly outperforms previous exact DHCP algorithms including an algorithm based on the award-winning Concorde TSP algorithm.</Para></Abstract></ChapterHeader><NoBody></NoBody></Chapter></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>A SAT Based Effective Algorithm for the Directed Hamiltonian Cycle Problem</title></titleInfo><titleInfo type="alternative" contentType="CDATA"><title>A SAT Based Effective Algorithm for the Directed Hamiltonian Cycle Problem</title></titleInfo><name type="personal"><namePart type="given">Gerold</namePart><namePart type="family">Jäger</namePart><affiliation>Computer Science Institute, Christian-Albrechts-University of Kiel, D-24118, Kiel, Germany</affiliation><affiliation>E-mail: gej@informatik.uni-kiel.de</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Weixiong</namePart><namePart type="family">Zhang</namePart><affiliation>Department of Computer Science/Department of Genetics, Washington University, 63130-4899, St. Louis, Missouri, United States</affiliation><affiliation>E-mail: weixiong.zhang@wustl.edu</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre displayLabel="OriginalPaper" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" type="conference" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-BFHXPBJJ-3">conference</genre><originInfo><publisher>Springer Berlin Heidelberg</publisher><place><placeTerm type="text">Berlin, Heidelberg</placeTerm></place><dateIssued encoding="w3cdtf">2010</dateIssued><copyrightDate encoding="w3cdtf">2010</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><abstract lang="en">Abstract: The Hamiltonian cycle problem (HCP) is an important combinatorial problem with applications in many areas. While thorough theoretical and experimental analyses have been made on the HCP in undirected graphs, little is known for the HCP in directed graphs (DHCP). The contribution of this work is an effective algorithm for the DHCP. Our algorithm explores and exploits the close relationship between the DHCP and the Assignment Problem (AP) and utilizes a technique based on Boolean satisfiability (SAT). By combining effective algorithms for the AP and SAT, our algorithm significantly outperforms previous exact DHCP algorithms including an algorithm based on the award-winning Concorde TSP algorithm.</abstract><relatedItem type="host"><titleInfo><title>Computer Science – Theory and Applications</title><subTitle>5th International Computer Science Symposium in Russia, CSR 2010, Kazan, Russia, June 16-20, 2010. Proceedings</subTitle></titleInfo><name type="personal"><namePart type="given">Farid</namePart><namePart type="family">Ablayev</namePart><affiliation>Dept. of Theoretical Cybernetics, Kazan State University, 420008, Kazan, Russia</affiliation><affiliation>E-mail: ablayev@ksu.ru</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Ernst</namePart><namePart type="given">W.</namePart><namePart type="family">Mayr</namePart><affiliation>Institut für Informatik, Technische Universität München, 85748, Garching, Germany</affiliation><affiliation>E-mail: mayr@in.tum.de</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><genre type="book-series" authority="ISTEX" authorityURI="https://publication-type.data.istex.fr" valueURI="https://publication-type.data.istex.fr/ark:/67375/JMC-0G6R5W5T-Z">book-series</genre><originInfo><publisher>Springer</publisher><copyrightDate 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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 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