Exact Algorithms for Maximum Acyclic Subgraph on a Superclass of Cubic Graphs
Identifieur interne : 001709 ( Istex/Corpus ); précédent : 001708; suivant : 001710Exact Algorithms for Maximum Acyclic Subgraph on a Superclass of Cubic Graphs
Auteurs : Henning Fernau ; Daniel RaibleSource :
- Lecture Notes in Computer Science [ 0302-9743 ] ; 2008.
Abstract
Abstract: Finding a maximum acyclic subgraph is on the list of problems that seem to be hard to tackle from a parameterized perspective. We develop two quite efficient algorithms (one is exact, the other parameterized) for (1,n)-graphs, a class containing cubic graphs. The running times are $\mathcal{O}^*(1.1871^m)$ and $\mathcal{O}^*(1.212^k)$ , respectively, determined by an amortized analysis via a non-standard measure.
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DOI: 10.1007/978-3-540-77891-2_14
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We develop two quite efficient algorithms (one is exact, the other parameterized) for (1,n)-graphs, a class containing cubic graphs. The running times are $\mathcal{O}^*(1.1871^m)$ and $\mathcal{O}^*(1.212^k)$ , respectively, determined by an amortized analysis via a non-standard measure.</div></front></TEI><istex><corpusName>springer</corpusName><author><json:item><name>Henning Fernau</name><affiliations><json:string>Univ.Trier, FB 4—Abteilung Informatik, 54286, Trier, Germany</json:string><json:string>E-mail: fernau@uni-trier.de</json:string></affiliations></json:item><json:item><name>Daniel Raible</name><affiliations><json:string>Univ.Trier, FB 4—Abteilung Informatik, 54286, Trier, Germany</json:string><json:string>E-mail: raible@uni-trier.de</json:string></affiliations></json:item></author><language><json:string>eng</json:string></language><originalGenre><json:string>OriginalPaper</json:string></originalGenre><abstract>Abstract: Finding a maximum acyclic subgraph is on the list of problems that seem to be hard to tackle from a parameterized perspective. We develop two quite efficient algorithms (one is exact, the other parameterized) for (1,n)-graphs, a class containing cubic graphs. The running times are $\mathcal{O}^*(1.1871^m)$ and $\mathcal{O}^*(1.212^k)$ , respectively, determined by an amortized analysis via a non-standard measure.</abstract><qualityIndicators><score>7.22</score><pdfVersion>1.6</pdfVersion><pdfPageSize>430 x 660 pts</pdfPageSize><refBibsNative>false</refBibsNative><keywordCount>0</keywordCount><abstractCharCount>426</abstractCharCount><pdfWordCount>6340</pdfWordCount><pdfCharCount>27873</pdfCharCount><pdfPageCount>13</pdfPageCount><abstractWordCount>60</abstractWordCount></qualityIndicators><title>Exact Algorithms for Maximum Acyclic Subgraph on a Superclass of Cubic Graphs</title><chapterId><json:string>14</json:string><json:string>Chap14</json:string></chapterId><refBibs><json:item><author></author><host><author></author><title>decrease k by w k ((u, w)), k by w k</title></host><title>A form an undirected 2-cycle then let z = arg min{w k (a), w k (b)}, decrease k by w k (z), k by w k (z), take z into MAS and delete z. 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We develop two quite efficient algorithms (one is exact, the other parameterized) for (1,n)-graphs, a class containing cubic graphs. The running times are $\mathcal{O}^*(1.1871^m)$ and $\mathcal{O}^*(1.212^k)$ , respectively, determined by an amortized analysis via a non-standard measure.</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>I17028</label><label>I1701X</label><label>I13022</label><label>I22013</label><label>I23050</label><item><term>Computer Science</term></item><item><term>Algorithm Analysis and Problem Complexity</term></item><item><term>Discrete Mathematics in Computer Science</term></item><item><term>Numeric Computing</term></item><item><term>Computer Communication Networks</term></item><item><term>Computer Graphics</term></item><item><term>Computational Biology/Bioinformatics</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="2008">Published</change><change xml:id="refBibs-istex" who="#ISTEX-API" when="2016-11-22">References added</change><change xml:id="refBibs-istex" who="#ISTEX-API" when="2017-01-20">References added</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><extension>txt</extension><original>false</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/document/0B0A4966CAED3C135475930A4DB3E3CBBBDEF416/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="Springer, Publisher found" wicri:toSee="no header"><istex:xmlDeclaration>version="1.0" encoding="UTF-8"</istex:xmlDeclaration><istex:docType PUBLIC="-//Springer-Verlag//DTD A++ V2.4//EN" URI="http://devel.springer.de/A++/V2.4/DTD/A++V2.4.dtd" name="istex:docType"></istex:docType><istex:document><Publisher><PublisherInfo><PublisherName>Springer Berlin Heidelberg</PublisherName><PublisherLocation>Berlin, Heidelberg</PublisherLocation></PublisherInfo><Series><SeriesInfo SeriesType="Series" TocLevels="0"><SeriesID>558</SeriesID><SeriesPrintISSN>0302-9743</SeriesPrintISSN><SeriesElectronicISSN>1611-3349</SeriesElectronicISSN><SeriesTitle Language="En">Lecture Notes in Computer Science</SeriesTitle></SeriesInfo><SeriesHeader><EditorGroup><Editor><EditorName DisplayOrder="Western"><GivenName>David</GivenName><FamilyName>Hutchison</FamilyName></EditorName></Editor><Editor><EditorName DisplayOrder="Western"><GivenName>Takeo</GivenName><FamilyName>Kanade</FamilyName></EditorName></Editor><Editor><EditorName DisplayOrder="Western"><GivenName>Josef</GivenName><FamilyName>Kittler</FamilyName></EditorName></Editor><Editor><EditorName DisplayOrder="Western"><GivenName>Jon</GivenName><GivenName>M.</GivenName><FamilyName>Kleinberg</FamilyName></EditorName></Editor><Editor><EditorName DisplayOrder="Western"><GivenName>Friedemann</GivenName><FamilyName>Mattern</FamilyName></EditorName></Editor><Editor><EditorName DisplayOrder="Western"><GivenName>John</GivenName><GivenName>C.</GivenName><FamilyName>Mitchell</FamilyName></EditorName></Editor><Editor><EditorName DisplayOrder="Western"><GivenName>Moni</GivenName><FamilyName>Naor</FamilyName></EditorName></Editor><Editor><EditorName DisplayOrder="Western"><GivenName>Oscar</GivenName><FamilyName>Nierstrasz</FamilyName></EditorName></Editor><Editor><EditorName DisplayOrder="Western"><GivenName>C.</GivenName><FamilyName>Pandu Rangan</FamilyName></EditorName></Editor><Editor><EditorName DisplayOrder="Western"><GivenName>Bernhard</GivenName><FamilyName>Steffen</FamilyName></EditorName></Editor><Editor><EditorName DisplayOrder="Western"><GivenName>Madhu</GivenName><FamilyName>Sudan</FamilyName></EditorName></Editor><Editor><EditorName DisplayOrder="Western"><GivenName>Demetri</GivenName><FamilyName>Terzopoulos</FamilyName></EditorName></Editor><Editor><EditorName DisplayOrder="Western"><GivenName>Doug</GivenName><FamilyName>Tygar</FamilyName></EditorName></Editor><Editor><EditorName DisplayOrder="Western"><GivenName>Moshe</GivenName><GivenName>Y.</GivenName><FamilyName>Vardi</FamilyName></EditorName></Editor><Editor><EditorName DisplayOrder="Western"><GivenName>Gerhard</GivenName><FamilyName>Weikum</FamilyName></EditorName></Editor></EditorGroup></SeriesHeader><Book Language="En"><BookInfo BookProductType="Proceedings" ContainsESM="No" Language="En" MediaType="eBook" NumberingStyle="Unnumbered" OutputMedium="All" TocLevels="0"><BookID>978-3-540-77891-2</BookID><BookTitle>WALCOM: Algorithms and Computation</BookTitle><BookSubTitle>Second International Workshop, WALCOM 2008, Dhaka, Bangladesh, February 7-8, 2008. Proceedings</BookSubTitle><BookVolumeNumber>4921</BookVolumeNumber><BookSequenceNumber>4921</BookSequenceNumber><BookDOI>10.1007/978-3-540-77891-2</BookDOI><BookTitleID>159662</BookTitleID><BookPrintISBN>978-3-540-77890-5</BookPrintISBN><BookElectronicISBN>978-3-540-77891-2</BookElectronicISBN><BookChapterCount>22</BookChapterCount><BookCopyright><CopyrightHolderName>Springer-Verlag Berlin Heidelberg</CopyrightHolderName><CopyrightYear>2008</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="I17028" Priority="2" Type="Secondary">Discrete Mathematics in Computer Science</BookSubject><BookSubject Code="I1701X" Priority="3" Type="Secondary">Numeric Computing</BookSubject><BookSubject Code="I13022" Priority="4" Type="Secondary">Computer Communication Networks</BookSubject><BookSubject Code="I22013" Priority="5" Type="Secondary">Computer Graphics</BookSubject><BookSubject Code="I23050" Priority="6" Type="Secondary">Computational Biology/Bioinformatics</BookSubject><SubjectCollection Code="SUCO11645">Computer Science</SubjectCollection></BookSubjectGroup></BookInfo><BookHeader><EditorGroup><Editor><EditorName DisplayOrder="Western"><GivenName>Shin-ichi</GivenName><FamilyName>Nakano</FamilyName></EditorName><Contact><Email>nakano@cs.gunma-u.ac.jp</Email></Contact></Editor><Editor><EditorName DisplayOrder="Western"><GivenName>Md.</GivenName><GivenName>Saidur</GivenName><FamilyName>Rahman</FamilyName></EditorName><Contact><Email>saidurrahman@cse.buet.ac.bd</Email></Contact></Editor></EditorGroup></BookHeader><Part ID="Part4"><PartInfo TocLevels="0"><PartID>4</PartID><PartSequenceNumber>4</PartSequenceNumber><PartTitle>Graph Algorithms I</PartTitle><PartChapterCount>3</PartChapterCount><PartContext><SeriesID>558</SeriesID><BookTitle>WALCOM: Algorithms and Computation</BookTitle></PartContext></PartInfo><Chapter ID="Chap14" Language="En"><ChapterInfo ChapterType="OriginalPaper" ContainsESM="No" NumberingStyle="Unnumbered" TocLevels="0"><ChapterID>14</ChapterID><ChapterDOI>10.1007/978-3-540-77891-2_14</ChapterDOI><ChapterSequenceNumber>14</ChapterSequenceNumber><ChapterTitle Language="En">Exact Algorithms for Maximum Acyclic Subgraph on a Superclass of Cubic Graphs</ChapterTitle><ChapterFirstPage>144</ChapterFirstPage><ChapterLastPage>156</ChapterLastPage><ChapterCopyright><CopyrightHolderName>Springer-Verlag Berlin Heidelberg</CopyrightHolderName><CopyrightYear>2008</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><PartID>4</PartID><BookID>978-3-540-77891-2</BookID><BookTitle>WALCOM: Algorithms and Computation</BookTitle></ChapterContext></ChapterInfo><ChapterHeader><AuthorGroup><Author AffiliationIDS="Aff1"><AuthorName DisplayOrder="Western"><GivenName>Henning</GivenName><FamilyName>Fernau</FamilyName></AuthorName><Contact><Email>fernau@uni-trier.de</Email></Contact></Author><Author AffiliationIDS="Aff1"><AuthorName DisplayOrder="Western"><GivenName>Daniel</GivenName><FamilyName>Raible</FamilyName></AuthorName><Contact><Email>raible@uni-trier.de</Email></Contact></Author><Affiliation ID="Aff1"><OrgName>Univ.Trier</OrgName><OrgAddress><Street>FB 4—Abteilung Informatik</Street><Postcode>54286</Postcode><City>Trier</City><Country>Germany</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>Finding a maximum acyclic subgraph is on the list of problems that seem to be hard to tackle from a parameterized perspective. We develop two quite efficient algorithms (one is exact, the other parameterized) for (1,<Emphasis Type="Italic">n</Emphasis>)-graphs, a class containing cubic graphs. The running times are <InlineEquation ID="IEq1"><InlineMediaObject><ImageObject FileRef="978-3-540-77891-2_14_Chapter_TeX2GIFIEq1.gif" Format="GIF" Color="BlackWhite" Type="Linedraw" Rendition="HTML"></ImageObject></InlineMediaObject><EquationSource Format="TEX">$\mathcal{O}^*(1.1871^m)$</EquationSource></InlineEquation> and <InlineEquation ID="IEq2"><InlineMediaObject><ImageObject FileRef="978-3-540-77891-2_14_Chapter_TeX2GIFIEq2.gif" Format="GIF" Color="BlackWhite" Type="Linedraw" Rendition="HTML"></ImageObject></InlineMediaObject><EquationSource Format="TEX">$\mathcal{O}^*(1.212^k)$</EquationSource></InlineEquation>, respectively, determined by an amortized analysis via a non-standard measure.</Para></Abstract></ChapterHeader><NoBody></NoBody></Chapter></Part></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Exact Algorithms for Maximum Acyclic Subgraph on a Superclass of Cubic Graphs</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Exact Algorithms for Maximum Acyclic Subgraph on a Superclass of Cubic Graphs</title></titleInfo><name type="personal"><namePart type="given">Henning</namePart><namePart type="family">Fernau</namePart><affiliation>Univ.Trier, FB 4—Abteilung Informatik, 54286, Trier, Germany</affiliation><affiliation>E-mail: fernau@uni-trier.de</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Daniel</namePart><namePart type="family">Raible</namePart><affiliation>Univ.Trier, FB 4—Abteilung Informatik, 54286, Trier, Germany</affiliation><affiliation>E-mail: raible@uni-trier.de</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">2008</dateIssued><copyrightDate encoding="w3cdtf">2008</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: Finding a maximum acyclic subgraph is on the list of problems that seem to be hard to tackle from a parameterized perspective. We develop two quite efficient algorithms (one is exact, the other parameterized) for (1,n)-graphs, a class containing cubic graphs. The running times are $\mathcal{O}^*(1.1871^m)$ and $\mathcal{O}^*(1.212^k)$ , respectively, determined by an amortized analysis via a non-standard measure.</abstract><relatedItem type="host"><titleInfo><title>WALCOM: Algorithms and Computation</title><subTitle>Second International Workshop, WALCOM 2008, Dhaka, Bangladesh, February 7-8, 2008. 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type="family">Weikum</namePart><role><roleTerm type="text">editor</roleTerm></role></name><originInfo><copyrightDate encoding="w3cdtf">2008</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-Verlag Berlin Heidelberg, 2008</recordOrigin></recordInfo></relatedItem><identifier type="istex">0B0A4966CAED3C135475930A4DB3E3CBBBDEF416</identifier><identifier type="DOI">10.1007/978-3-540-77891-2_14</identifier><identifier type="ChapterID">14</identifier><identifier type="ChapterID">Chap14</identifier><accessCondition type="use and reproduction" contentType="copyright">Springer-Verlag Berlin Heidelberg, 2008</accessCondition><recordInfo><recordContentSource>SPRINGER</recordContentSource><recordOrigin>Springer-Verlag Berlin Heidelberg, 2008</recordOrigin></recordInfo></mods></metadata></istex></record>Pour manipuler ce 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