Combining Two Worlds: Parameterised Approximation for Vertex Cover
Identifieur interne : 001084 ( Istex/Corpus ); précédent : 001083; suivant : 001085Combining Two Worlds: Parameterised Approximation for Vertex Cover
Auteurs : Ljiljana Brankovic ; Henning FernauSource :
- Lecture Notes in Computer Science [ 0302-9743 ] ; 2010.
Abstract
Abstract: We explore opportunities for parameterising constant factor approximation algorithms for vertex cover. We provide a simple algorithm that works on any approximation ratio of the form $\frac {2l+1}{l+1}$ and has complexity that outperforms an algorithm by Bourgeois et al. derived from a sophisticated exact parameterised algorithm. In particular, for l = 1 (factor 1.5 approximation) our algorithm runs in time $\mathcal{O}^{*}(1.09^{k})$ . Additionally, we present an improved polynomial-time approximation algorithm for graphs of average degree four.
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DOI: 10.1007/978-3-642-17517-6_35
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We provide a simple algorithm that works on any approximation ratio of the form $\frac {2l+1}{l+1}$ and has complexity that outperforms an algorithm by Bourgeois et al. derived from a sophisticated exact parameterised algorithm. In particular, for l = 1 (factor 1.5 approximation) our algorithm runs in time $\mathcal{O}^{*}(1.09^{k})$ . Additionally, we present an improved polynomial-time approximation algorithm for graphs of average degree four.</div></front></TEI><istex><corpusName>springer</corpusName><author><json:item><name>Ljiljana Brankovic</name><affiliations><json:string>School of Electrical Engineering and Computer Science, The University of Newcastle, 2308, Callaghan, NSW, Australia</json:string><json:string>E-mail: Ljiljana.Brankovic@newcastle.edu.au</json:string></affiliations></json:item><json:item><name>Henning Fernau</name><affiliations><json:string>Fachbereich 4, Abteilung Informatik, Universität Trier, 54286, Trier, Germany</json:string><json:string>E-mail: fernau@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: We explore opportunities for parameterising constant factor approximation algorithms for vertex cover. We provide a simple algorithm that works on any approximation ratio of the form $\frac {2l+1}{l+1}$ and has complexity that outperforms an algorithm by Bourgeois et al. derived from a sophisticated exact parameterised algorithm. In particular, for l = 1 (factor 1.5 approximation) our algorithm runs in time $\mathcal{O}^{*}(1.09^{k})$ . Additionally, we present an improved polynomial-time approximation algorithm for graphs of average degree four.</abstract><qualityIndicators><score>5.9</score><pdfVersion>1.3</pdfVersion><pdfPageSize>429.725 x 659.895 pts</pdfPageSize><refBibsNative>false</refBibsNative><keywordCount>0</keywordCount><abstractCharCount>562</abstractCharCount><pdfWordCount>6737</pdfWordCount><pdfCharCount>30719</pdfCharCount><pdfPageCount>13</pdfPageCount><abstractWordCount>75</abstractWordCount></qualityIndicators><title>Combining Two Worlds: Parameterised Approximation for Vertex Cover</title><chapterId><json:string>35</json:string><json:string>Chap35</json:string></chapterId><refBibs><json:item><author><json:item><name>R Bar-Yehuda</name></json:item></author><host><volume>27</volume><pages><last>144</last><first>131</first></pages><author></author><title>Algorithmica</title><publicationDate>2000</publicationDate></host><title>One for the price of two: a unified approach for approximating covering problems</title><publicationDate>2000</publicationDate></json:item><json:item><author><json:item><name>P Berman</name></json:item><json:item><name>T Fujito</name></json:item></author><host><pages><last>460</last><first>449</first></pages><author></author><title>WADS 1995</title><publicationDate>1995</publicationDate></host><title>On approximation properties of the independent set problem for degree 3 graphs</title><publicationDate>1995</publicationDate></json:item><json:item><author><json:item><name>N Bourgeois</name></json:item><json:item><name>B Escoffier</name></json:item><json:item><name>V,T Paschos</name></json:item></author><host><pages><last>518</last><first>507</first></pages><author></author><title>WADS 2009</title><publicationDate>2009</publicationDate></host><title>Efficient approximation of combinatorial problems by moderately exponential algorithms</title><publicationDate>2009</publicationDate></json:item><json:item><author><json:item><name>L Cai</name></json:item><json:item><name>X Huang</name></json:item></author><host><volume>57</volume><pages><last>412</last><first>398</first></pages><issue>2</issue><author></author><title>Algorithmica</title><publicationDate>2010</publicationDate></host><title>Fixed-Parameter Approximation: Conceptual Framework and Approximability Results</title><publicationDate>2010</publicationDate></json:item><json:item><author><json:item><name>L Cai</name></json:item><json:item><name>D Juedes</name></json:item></author><host><volume>67</volume><pages><last>807</last><first>789</first></pages><author></author><title>J. 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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>2010</copyrightDate></serie><host><editor><json:item><name>Otfried Cheong</name><affiliations><json:string>Department of Computer Science, KAIST, Gwahangno 335, 305-701, Yuseong-gu, Daejeon, Korea</json:string><json:string>E-mail: otfried@kaist.edu</json:string></affiliations></json:item><json:item><name>Kyung-Yong Chwa</name><affiliations><json:string>Department of Computer Science, KAIST, Gwahangno 335, 305-701, Yuseong-gu, Daejeon, Korea</json:string><json:string>E-mail: kychwa@jupiter.kaist.ac.kr</json:string></affiliations></json:item><json:item><name>Kunsoo Park</name><affiliations><json:string>School of Computer Science and Engineering, Seoul National University, 151-742, Seoul, Korea</json:string><json:string>E-mail: kpark@snu.ac.kr</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>Discrete Mathematics in Computer Science</value></json:item><json:item><value>Computer Communication Networks</value></json:item><json:item><value>Computer Graphics</value></json:item><json:item><value>Data Structures</value></json:item><json:item><value>Numeric 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Heidelberg</publisher><pubPlace>Berlin, Heidelberg</pubPlace><date type="published" when="2010"></date><biblScope unit="volume">6506</biblScope><biblScope unit="page" from="390">390</biblScope><biblScope unit="page" to="402">402</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>2010</date></biblScope><idno type="pISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="series-Id">558</idno></series><idno type="istex">FFED7303E265FCB52EFA0AF797CBD4F935EACDC4</idno><idno type="DOI">10.1007/978-3-642-17517-6_35</idno><idno type="ChapterID">35</idno><idno type="ChapterID">Chap35</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>2010</date></creation><langUsage><language ident="en">en</language></langUsage><abstract xml:lang="en"><p>Abstract: We explore opportunities for parameterising constant factor approximation algorithms for vertex cover. We provide a simple algorithm that works on any approximation ratio of the form $\frac {2l+1}{l+1}$ and has complexity that outperforms an algorithm by Bourgeois et al. derived from a sophisticated exact parameterised algorithm. In particular, for l = 1 (factor 1.5 approximation) our algorithm runs in time $\mathcal{O}^{*}(1.09^{k})$ . Additionally, we present an improved polynomial-time approximation algorithm for graphs of average degree four.</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>I13022</label><label>I22013</label><label>I15017</label><label>I1701X</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>Computer Communication Networks</term></item><item><term>Computer Graphics</term></item><item><term>Data Structures</term></item><item><term>Numeric Computing</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="2010">Published</change><change xml:id="refBibs-istex" who="#ISTEX-API" 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University</OrgName><OrgAddress><City>Pittsburgh</City><State>PA</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff3"><OrgName>University of Surrey</OrgName><OrgAddress><City>Guildford</City><Country>UK</Country></OrgAddress></Affiliation><Affiliation ID="Aff4"><OrgName>Cornell University</OrgName><OrgAddress><City>Ithaca</City><State>NY</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff5"><OrgName>ETH Zurich</OrgName><OrgAddress><City>Zurich</City><Country>Switzerland</Country></OrgAddress></Affiliation><Affiliation ID="Aff6"><OrgName>Stanford University</OrgName><OrgAddress><City>Stanford</City><State>CA</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff7"><OrgName>Weizmann Institute of 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>978-3-642-17517-6</BookID><BookTitle>Algorithms and Computation</BookTitle><BookSubTitle>21st International Symposium, ISAAC 2010, Jeju Island, Korea, December 15-17, 2010, Proceedings, Part I</BookSubTitle><BookVolumeNumber>6506</BookVolumeNumber><BookSequenceNumber>6506</BookSequenceNumber><BookDOI>10.1007/978-3-642-17517-6</BookDOI><BookTitleID>215423</BookTitleID><BookPrintISBN>978-3-642-17516-9</BookPrintISBN><BookElectronicISBN>978-3-642-17517-6</BookElectronicISBN><BookChapterCount>40</BookChapterCount><BookCopyright><CopyrightHolderName>Springer 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="I17028" Priority="2" Type="Secondary">Discrete Mathematics in Computer Science</BookSubject><BookSubject Code="I13022" Priority="3" Type="Secondary">Computer Communication Networks</BookSubject><BookSubject Code="I22013" Priority="4" Type="Secondary">Computer Graphics</BookSubject><BookSubject Code="I15017" Priority="5" Type="Secondary">Data Structures</BookSubject><BookSubject Code="I1701X" Priority="6" Type="Secondary">Numeric Computing</BookSubject><SubjectCollection Code="SUCO11645">Computer Science</SubjectCollection></BookSubjectGroup><BookContext><SeriesID>558</SeriesID></BookContext></BookInfo><BookHeader><EditorGroup><Editor AffiliationIDS="Aff16"><EditorName DisplayOrder="Western"><GivenName>Otfried</GivenName><FamilyName>Cheong</FamilyName></EditorName><Contact><Email>otfried@kaist.edu</Email></Contact></Editor><Editor AffiliationIDS="Aff16"><EditorName DisplayOrder="Western"><GivenName>Kyung-Yong</GivenName><FamilyName>Chwa</FamilyName></EditorName><Contact><Email>kychwa@jupiter.kaist.ac.kr</Email></Contact></Editor><Editor AffiliationIDS="Aff17"><EditorName DisplayOrder="Western"><GivenName>Kunsoo</GivenName><FamilyName>Park</FamilyName></EditorName><Contact><Email>kpark@snu.ac.kr</Email></Contact></Editor><Affiliation ID="Aff16"><OrgDivision>Department of Computer Science</OrgDivision><OrgName>KAIST</OrgName><OrgAddress><Street>Gwahangno 335</Street><Postcode>305-701</Postcode><City>Yuseong-gu</City><State>Daejeon</State><Country>Korea</Country></OrgAddress></Affiliation><Affiliation ID="Aff17"><OrgDivision>School of Computer Science and Engineering</OrgDivision><OrgName>Seoul National University</OrgName><OrgAddress><Postcode>151-742</Postcode><City>Seoul</City><Country>Korea</Country></OrgAddress></Affiliation></EditorGroup></BookHeader><Part ID="Part10"><PartInfo TocLevels="0"><PartID>10</PartID><PartSequenceNumber>10</PartSequenceNumber><PartTitle>Session 5A. Fixed Parameter Tractability</PartTitle><PartChapterCount>4</PartChapterCount><PartContext><SeriesID>558</SeriesID><BookTitle>Algorithms and Computation</BookTitle></PartContext></PartInfo><Chapter ID="Chap35" Language="En"><ChapterInfo ChapterType="OriginalPaper" ContainsESM="No" NumberingDepth="2" NumberingStyle="ContentOnly" TocLevels="0"><ChapterID>35</ChapterID><ChapterDOI>10.1007/978-3-642-17517-6_35</ChapterDOI><ChapterSequenceNumber>35</ChapterSequenceNumber><ChapterTitle Language="En">Combining Two Worlds: Parameterised Approximation for Vertex Cover</ChapterTitle><ChapterFirstPage>390</ChapterFirstPage><ChapterLastPage>402</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><PartID>10</PartID><BookID>978-3-642-17517-6</BookID><BookTitle>Algorithms and Computation</BookTitle></ChapterContext></ChapterInfo><ChapterHeader><AuthorGroup><Author AffiliationIDS="Aff18"><AuthorName DisplayOrder="Western"><GivenName>Ljiljana</GivenName><FamilyName>Brankovic</FamilyName></AuthorName><Contact><Email>Ljiljana.Brankovic@newcastle.edu.au</Email></Contact></Author><Author AffiliationIDS="Aff19"><AuthorName DisplayOrder="Western"><GivenName>Henning</GivenName><FamilyName>Fernau</FamilyName></AuthorName><Contact><Email>fernau@uni-trier.de</Email></Contact></Author><Affiliation ID="Aff18"><OrgDivision>School of Electrical Engineering and Computer Science</OrgDivision><OrgName>The University of Newcastle</OrgName><OrgAddress><City>Callaghan</City><State>NSW</State><Postcode>2308</Postcode><Country>Australia</Country></OrgAddress></Affiliation><Affiliation ID="Aff19"><OrgDivision>Fachbereich 4, Abteilung Informatik</OrgDivision><OrgName>Universität Trier</OrgName><OrgAddress><Postcode>54286</Postcode><City>Trier</City><Country>Germany</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>We explore opportunities for parameterising constant factor approximation algorithms for vertex cover. We provide a simple algorithm that works on any approximation ratio of the form <InlineEquation ID="IEq1"><InlineMediaObject><ImageObject FileRef="978-3-642-17517-6_35_Chapter_TeX2GIFIEq1.gif" Format="GIF" Color="BlackWhite" Type="Linedraw" Rendition="HTML"></ImageObject></InlineMediaObject><EquationSource Format="TEX">$\frac {2l+1}{l+1}$</EquationSource></InlineEquation> and has complexity that outperforms an algorithm by Bourgeois et al. derived from a sophisticated exact parameterised algorithm. In particular, for <Emphasis Type="Italic">l</Emphasis> = 1 (factor 1.5 approximation) our algorithm runs in time <InlineEquation ID="IEq2"><InlineMediaObject><ImageObject FileRef="978-3-642-17517-6_35_Chapter_TeX2GIFIEq2.gif" Format="GIF" Color="BlackWhite" Type="Linedraw" Rendition="HTML"></ImageObject></InlineMediaObject><EquationSource Format="TEX">$\mathcal{O}^{*}(1.09^{k})$</EquationSource></InlineEquation>. Additionally, we present an improved polynomial-time approximation algorithm for graphs of average degree four.</Para></Abstract></ChapterHeader><NoBody></NoBody></Chapter></Part></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Combining Two Worlds: Parameterised Approximation for Vertex Cover</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Combining Two Worlds: Parameterised Approximation for Vertex Cover</title></titleInfo><name type="personal"><namePart type="given">Ljiljana</namePart><namePart type="family">Brankovic</namePart><affiliation>School of Electrical Engineering and Computer Science, The University of Newcastle, 2308, Callaghan, NSW, Australia</affiliation><affiliation>E-mail: Ljiljana.Brankovic@newcastle.edu.au</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Henning</namePart><namePart type="family">Fernau</namePart><affiliation>Fachbereich 4, Abteilung Informatik, Universität Trier, 54286, Trier, Germany</affiliation><affiliation>E-mail: fernau@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">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><physicalDescription><internetMediaType>text/html</internetMediaType></physicalDescription><abstract lang="en">Abstract: We explore opportunities for parameterising constant factor approximation algorithms for vertex cover. We provide a simple algorithm that works on any approximation ratio of the form $\frac {2l+1}{l+1}$ and has complexity that outperforms an algorithm by Bourgeois et al. derived from a sophisticated exact parameterised algorithm. In particular, for l = 1 (factor 1.5 approximation) our algorithm runs in time $\mathcal{O}^{*}(1.09^{k})$ . Additionally, we present an improved polynomial-time approximation algorithm for graphs of average degree four.</abstract><relatedItem type="host"><titleInfo><title>Algorithms and Computation</title><subTitle>21st International Symposium, ISAAC 2010, Jeju Island, Korea, December 15-17, 2010, Proceedings, Part I</subTitle></titleInfo><name type="personal"><namePart type="given">Otfried</namePart><namePart type="family">Cheong</namePart><affiliation>Department of Computer Science, KAIST, Gwahangno 335, 305-701, Yuseong-gu, Daejeon, Korea</affiliation><affiliation>E-mail: otfried@kaist.edu</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Kyung-Yong</namePart><namePart type="family">Chwa</namePart><affiliation>Department of Computer Science, KAIST, Gwahangno 335, 305-701, Yuseong-gu, Daejeon, Korea</affiliation><affiliation>E-mail: kychwa@jupiter.kaist.ac.kr</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Kunsoo</namePart><namePart type="family">Park</namePart><affiliation>School of Computer Science and Engineering, Seoul National University, 151-742, Seoul, Korea</affiliation><affiliation>E-mail: kpark@snu.ac.kr</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><genre type="book-series" displayLabel="Proceedings"></genre><originInfo><copyrightDate encoding="w3cdtf">2010</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="I17028">Discrete Mathematics in Computer Science</topic><topic authority="SpringerSubjectCodes" authorityURI="I13022">Computer Communication Networks</topic><topic authority="SpringerSubjectCodes" authorityURI="I22013">Computer Graphics</topic><topic authority="SpringerSubjectCodes" authorityURI="I15017">Data Structures</topic><topic authority="SpringerSubjectCodes" authorityURI="I1701X">Numeric Computing</topic></subject><identifier type="DOI">10.1007/978-3-642-17517-6</identifier><identifier type="ISBN">978-3-642-17516-9</identifier><identifier type="eISBN">978-3-642-17517-6</identifier><identifier type="ISSN">0302-9743</identifier><identifier type="eISSN">1611-3349</identifier><identifier type="BookTitleID">215423</identifier><identifier type="BookID">978-3-642-17517-6</identifier><identifier type="BookChapterCount">40</identifier><identifier type="BookVolumeNumber">6506</identifier><identifier type="BookSequenceNumber">6506</identifier><identifier type="PartChapterCount">4</identifier><part><date>2010</date><detail type="part"><title>Session 5A. 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