A Parameterized Perspective on Packing Paths of Length Two
Identifieur interne : 001808 ( Istex/Corpus ); précédent : 001807; suivant : 001809A Parameterized Perspective on Packing Paths of Length Two
Auteurs : Henning Fernau ; Daniel RaibleSource :
- Lecture Notes in Computer Science [ 0302-9743 ] ; 2008.
Abstract
Abstract: We study (vertex-disjoint) packings of paths of length two (i.e., of P 2’s) in graphs under a parameterized perspective. Starting from a maximal P 2-packing $\mathcal {P}$ of size j we use extremal combinatorial arguments for determining how many vertices of $\mathcal {P}$ appear in some P 2-packing of size (j + 1) (if it exists). We prove that one can ’reuse’ 2.5j vertices. Based on a WIN-WIN approach, we build an algorithm which decides if a P 2-packing of size at least k exists in a given graph in time ${\mathcal{O}}^*(2.482^{3k})$ .
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DOI: 10.1007/978-3-540-85097-7_6
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Starting from a maximal P 2-packing $\mathcal {P}$ of size j we use extremal combinatorial arguments for determining how many vertices of $\mathcal {P}$ appear in some P 2-packing of size (j + 1) (if it exists). We prove that one can ’reuse’ 2.5j vertices. 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Starting from a maximal P 2-packing $\mathcal {P}$ of size j we use extremal combinatorial arguments for determining how many vertices of $\mathcal {P}$ appear in some P 2-packing of size (j + 1) (if it exists). We prove that one can ’reuse’ 2.5j vertices. Based on a WIN-WIN approach, we build an algorithm which decides if a P 2-packing of size at least k exists in a given graph in time ${\mathcal{O}}^*(2.482^{3k})$ .</abstract><qualityIndicators><score>7.48</score><pdfVersion>1.6</pdfVersion><pdfPageSize>430 x 660 pts</pdfPageSize><refBibsNative>false</refBibsNative><keywordCount>0</keywordCount><abstractCharCount>552</abstractCharCount><pdfWordCount>4876</pdfWordCount><pdfCharCount>21001</pdfCharCount><pdfPageCount>10</pdfPageCount><abstractWordCount>92</abstractWordCount></qualityIndicators><title>A Parameterized Perspective on Packing Paths of Length Two</title><chapterId><json:string>6</json:string><json:string>Chap6</json:string></chapterId><refBibs><json:item><author><json:item><name>De Bontridder</name></json:item><json:item><name>K,M J Halldórsson</name></json:item><json:item><name>B,V Halldórsson</name></json:item><json:item><name>M,M Lenstra</name></json:item><json:item><name>J,K Ravi</name></json:item><json:item><name>R Stougie</name></json:item><json:item><name>L </name></json:item></author><host><volume>98</volume><pages><last>491</last><first>477</first></pages><author></author><title>Math. 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Proceedings</title><idno type="pISBN">978-3-540-85096-0</idno><idno type="eISBN">978-3-540-85097-7</idno><idno type="pISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="DOI">10.1007/978-3-540-85097-7</idno><idno type="book-ID">978-3-540-85097-7</idno><idno type="book-title-ID">176302</idno><idno type="book-sequence-number">5165</idno><idno type="book-volume-number">5165</idno><idno type="book-chapter-count">44</idno><editor><persName><forename type="first">Boting</forename><surname>Yang</surname></persName></editor><editor><persName><forename type="first">Ding-Zhu</forename><surname>Du</surname></persName></editor><editor><persName><forename type="first">Cao</forename><forename type="first">An</forename><surname>Wang</surname></persName></editor><imprint><publisher>Springer Berlin Heidelberg</publisher><pubPlace>Berlin, Heidelberg</pubPlace><date type="published" when="2008"></date><biblScope unit="volume">5165</biblScope><biblScope unit="page" from="54">54</biblScope><biblScope unit="page" to="63">63</biblScope></imprint></monogr><series><title level="s">Lecture Notes in Computer Science</title><editor><persName><forename type="first">David</forename><surname>Hutchison</surname></persName></editor><editor><persName><forename type="first">Takeo</forename><surname>Kanade</surname></persName></editor><editor><persName><forename type="first">Josef</forename><surname>Kittler</surname></persName></editor><editor><persName><forename type="first">Jon</forename><forename type="first">M.</forename><surname>Kleinberg</surname></persName></editor><editor><persName><forename type="first">Friedemann</forename><surname>Mattern</surname></persName></editor><editor><persName><forename type="first">John</forename><forename type="first">C.</forename><surname>Mitchell</surname></persName></editor><editor><persName><forename type="first">Moni</forename><surname>Naor</surname></persName></editor><editor><persName><forename type="first">Oscar</forename><surname>Nierstrasz</surname></persName></editor><editor><persName><forename type="first">C.</forename><surname>Pandu Rangan</surname></persName></editor><editor><persName><forename type="first">Bernhard</forename><surname>Steffen</surname></persName></editor><editor><persName><forename type="first">Madhu</forename><surname>Sudan</surname></persName></editor><editor><persName><forename type="first">Demetri</forename><surname>Terzopoulos</surname></persName></editor><editor><persName><forename type="first">Doug</forename><surname>Tygar</surname></persName></editor><editor><persName><forename type="first">Moshe</forename><forename type="first">Y.</forename><surname>Vardi</surname></persName></editor><editor><persName><forename type="first">Gerhard</forename><surname>Weikum</surname></persName></editor><biblScope><date>2008</date></biblScope><idno type="pISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="series-Id">558</idno></series><idno type="istex">BDC5A3E742BD46ACA1AD40E5FC9D392A3D7ABF81</idno><idno type="DOI">10.1007/978-3-540-85097-7_6</idno><idno type="ChapterID">6</idno><idno type="ChapterID">Chap6</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>2008</date></creation><langUsage><language ident="en">en</language></langUsage><abstract xml:lang="en"><p>Abstract: We study (vertex-disjoint) packings of paths of length two (i.e., of P 2’s) in graphs under a parameterized perspective. Starting from a maximal P 2-packing $\mathcal {P}$ of size j we use extremal combinatorial arguments for determining how many vertices of $\mathcal {P}$ appear in some P 2-packing of size (j + 1) (if it exists). We prove that one can ’reuse’ 2.5j vertices. Based on a WIN-WIN approach, we build an algorithm which decides if a P 2-packing of size at least k exists in a given graph in time ${\mathcal{O}}^*(2.482^{3k})$ .</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>M14018</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>Algorithms</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="2008">Published</change><change xml:id="refBibs-istex" who="#ISTEX-API" when="2016-11-23">References added</change><change xml:id="refBibs-istex" who="#ISTEX-API" when="2017-01-21">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/BDC5A3E742BD46ACA1AD40E5FC9D392A3D7ABF81/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>978-3-540-85097-7</BookID><BookTitle>Combinatorial Optimization and Applications</BookTitle><BookSubTitle>Second International Conference, COCOA 2008, St. John’s, NL, Canada, August 21-24, 2008. Proceedings</BookSubTitle><BookVolumeNumber>5165</BookVolumeNumber><BookSequenceNumber>5165</BookSequenceNumber><BookDOI>10.1007/978-3-540-85097-7</BookDOI><BookTitleID>176302</BookTitleID><BookPrintISBN>978-3-540-85096-0</BookPrintISBN><BookElectronicISBN>978-3-540-85097-7</BookElectronicISBN><BookChapterCount>44</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="M14018" Priority="6" Type="Secondary">Algorithms</BookSubject><SubjectCollection Code="SUCO11645">Computer Science</SubjectCollection></BookSubjectGroup></BookInfo><BookHeader><EditorGroup><Editor><EditorName DisplayOrder="Western"><GivenName>Boting</GivenName><FamilyName>Yang</FamilyName></EditorName><Contact><Email>boting@cs.uregina.ca</Email></Contact></Editor><Editor><EditorName DisplayOrder="Western"><GivenName>Ding-Zhu</GivenName><FamilyName>Du</FamilyName></EditorName><Contact><Email>dzdu@utdallas.edu</Email></Contact></Editor><Editor><EditorName DisplayOrder="Western"><GivenName>Cao</GivenName><GivenName>An</GivenName><FamilyName>Wang</FamilyName></EditorName><Contact><Email>wang@cs.mun.ca</Email></Contact></Editor></EditorGroup></BookHeader><Chapter ID="Chap6" Language="En"><ChapterInfo ChapterType="OriginalPaper" ContainsESM="No" NumberingStyle="Unnumbered" TocLevels="0"><ChapterID>6</ChapterID><ChapterDOI>10.1007/978-3-540-85097-7_6</ChapterDOI><ChapterSequenceNumber>6</ChapterSequenceNumber><ChapterTitle Language="En">A Parameterized Perspective on Packing Paths of Length Two</ChapterTitle><ChapterFirstPage>54</ChapterFirstPage><ChapterLastPage>63</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><BookID>978-3-540-85097-7</BookID><BookTitle>Combinatorial Optimization and Applications</BookTitle></ChapterContext></ChapterInfo><ChapterHeader><AuthorGroup><Author AffiliationIDS="Aff1"><AuthorName DisplayOrder="Western"><GivenName>Henning</GivenName><FamilyName>Fernau</FamilyName></AuthorName><Contact><Email>fernau@informatik.uni-trier.de</Email></Contact></Author><Author AffiliationIDS="Aff1"><AuthorName DisplayOrder="Western"><GivenName>Daniel</GivenName><FamilyName>Raible</FamilyName></AuthorName><Contact><Email>raible@informatik.uni-trier.de</Email></Contact></Author><Affiliation ID="Aff1"><OrgName>Universität Trier, FB IV—Abteilung Informatik</OrgName><OrgAddress><Postcode>54286</Postcode><City>Trier</City><Country>Germany</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>We study (vertex-disjoint) packings of paths of length two (i.e., of <Emphasis Type="Italic">P</Emphasis><Subscript>2</Subscript>’s) in graphs under a parameterized perspective. Starting from a maximal <Emphasis Type="Italic">P</Emphasis><Subscript>2</Subscript>-packing <InlineEquation ID="IEq1"><InlineMediaObject><ImageObject FileRef="978-3-540-85097-7_6_Chapter_TeX2GIFIEq1.gif" Format="GIF" Color="BlackWhite" Type="Linedraw" Rendition="HTML"></ImageObject></InlineMediaObject><EquationSource Format="TEX">$\mathcal {P}$</EquationSource></InlineEquation> of size <Emphasis Type="Italic">j</Emphasis> we use extremal combinatorial arguments for determining how many vertices of <InlineEquation ID="IEq2"><InlineMediaObject><ImageObject FileRef="978-3-540-85097-7_6_Chapter_TeX2GIFIEq2.gif" Format="GIF" Color="BlackWhite" Type="Linedraw" Rendition="HTML"></ImageObject></InlineMediaObject><EquationSource Format="TEX">$\mathcal {P}$</EquationSource></InlineEquation> appear in some <Emphasis Type="Italic">P</Emphasis><Subscript>2</Subscript>-packing of size (<Emphasis Type="Italic">j</Emphasis> + 1) (if it exists). We prove that one can ’reuse’ 2.5<Emphasis Type="Italic">j</Emphasis> vertices. Based on a WIN-WIN approach, we build an algorithm which decides if a <Emphasis Type="Italic">P</Emphasis><Subscript>2</Subscript>-packing of size at least <Emphasis Type="Italic">k</Emphasis> exists in a given graph in time <InlineEquation ID="IEq3"><InlineMediaObject><ImageObject FileRef="978-3-540-85097-7_6_Chapter_TeX2GIFIEq3.gif" Format="GIF" Color="BlackWhite" Type="Linedraw" Rendition="HTML"></ImageObject></InlineMediaObject><EquationSource Format="TEX">${\mathcal{O}}^*(2.482^{3k})$</EquationSource></InlineEquation>.</Para></Abstract></ChapterHeader><NoBody></NoBody></Chapter></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>A Parameterized Perspective on Packing Paths of Length Two</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>A Parameterized Perspective on Packing Paths of Length Two</title></titleInfo><name type="personal"><namePart type="given">Henning</namePart><namePart type="family">Fernau</namePart><affiliation>Universität Trier, FB IV—Abteilung Informatik, 54286, Trier, Germany</affiliation><affiliation>E-mail: fernau@informatik.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>Universität Trier, FB IV—Abteilung Informatik, 54286, Trier, Germany</affiliation><affiliation>E-mail: raible@informatik.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: We study (vertex-disjoint) packings of paths of length two (i.e., of P 2’s) in graphs under a parameterized perspective. Starting from a maximal P 2-packing $\mathcal {P}$ of size j we use extremal combinatorial arguments for determining how many vertices of $\mathcal {P}$ appear in some P 2-packing of size (j + 1) (if it exists). We prove that one can ’reuse’ 2.5j vertices. Based on a WIN-WIN approach, we build an algorithm which decides if a P 2-packing of size at least k exists in a given graph in time ${\mathcal{O}}^*(2.482^{3k})$ .</abstract><relatedItem type="host"><titleInfo><title>Combinatorial Optimization and Applications</title><subTitle>Second International Conference, COCOA 2008, St. John’s, NL, Canada, August 21-24, 2008. Proceedings</subTitle></titleInfo><name type="personal"><namePart type="given">Boting</namePart><namePart type="family">Yang</namePart><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Ding-Zhu</namePart><namePart type="family">Du</namePart><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Cao</namePart><namePart type="given">An</namePart><namePart type="family">Wang</namePart><role><roleTerm type="text">editor</roleTerm></role></name><genre type="book-series" displayLabel="Proceedings"></genre><originInfo><copyrightDate encoding="w3cdtf">2008</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 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