A Faster Exact Algorithm for the Directed Maximum Leaf Spanning Tree Problem
Identifieur interne : 001719 ( Istex/Corpus ); précédent : 001718; suivant : 001720A Faster Exact Algorithm for the Directed Maximum Leaf Spanning Tree Problem
Auteurs : Daniel Binkele-Raible ; Henning FernauSource :
- Lecture Notes in Computer Science [ 0302-9743 ] ; 2010.
Abstract
Abstract: Given a directed graph G = (V,A), the Directed Maximum Leaf Spanning Tree problem asks to compute a directed spanning tree with as many leaves as possible. By designing a branching algorithm analyzed with Measure&Conquer, we show that the problem can be solved in time ${\mathcal{O}}^*({1.9044}^n)$ using polynomial space. Allowing exponential space, this run time upper bound can be lowered to ${\mathcal{O}}^*(1.8139^n)$ .
Url:
DOI: 10.1007/978-3-642-13182-0_31
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By designing a branching algorithm analyzed with Measure&Conquer, we show that the problem can be solved in time ${\mathcal{O}}^*({1.9044}^n)$ using polynomial space. 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By designing a branching algorithm analyzed with Measure&Conquer, we show that the problem can be solved in time ${\mathcal{O}}^*({1.9044}^n)$ using polynomial space. 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Proceedings</title><idno type="pISBN">978-3-642-13181-3</idno><idno type="eISBN">978-3-642-13182-0</idno><idno type="pISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="DOI">10.1007/978-3-642-13182-0</idno><idno type="book-ID">978-3-642-13182-0</idno><idno type="book-title-ID">211548</idno><idno type="book-sequence-number">6072</idno><idno type="book-volume-number">6072</idno><idno type="book-chapter-count">38</idno><editor><persName><forename type="first">Farid</forename><surname>Ablayev</surname></persName><email>ablayev@ksu.ru</email><affiliation>Dept. of Theoretical Cybernetics, Kazan State University, 420008, Kazan, Russia</affiliation></editor><editor><persName><forename type="first">Ernst</forename><forename type="first">W.</forename><surname>Mayr</surname></persName><email>mayr@in.tum.de</email><affiliation>Institut für Informatik, Technische Universität München, 85748, Garching, Germany</affiliation></editor><imprint><publisher>Springer Berlin Heidelberg</publisher><pubPlace>Berlin, Heidelberg</pubPlace><date type="published" when="2010"></date><biblScope unit="volume">6072</biblScope><biblScope unit="page" from="328">328</biblScope><biblScope unit="page" to="339">339</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">92E8A85F6DE5A50D60C19FBA7ADF63DFAE8DB524</idno><idno type="DOI">10.1007/978-3-642-13182-0_31</idno><idno type="ChapterID">31</idno><idno type="ChapterID">Chap31</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>2010</date></creation><langUsage><language ident="en">en</language></langUsage><abstract xml:lang="en"><p>Abstract: Given a directed graph G = (V,A), the Directed Maximum Leaf Spanning Tree problem asks to compute a directed spanning tree with as many leaves as possible. By designing a branching algorithm analyzed with Measure&Conquer, we show that the problem can be solved in time ${\mathcal{O}}^*({1.9044}^n)$ using polynomial space. Allowing exponential space, this run time upper bound can be lowered to ${\mathcal{O}}^*(1.8139^n)$ .</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 Computing</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="2010">Published</change><change xml:id="refBibs-istex" 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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 AffiliationIDS="Aff1"><EditorName DisplayOrder="Western"><GivenName>David</GivenName><FamilyName>Hutchison</FamilyName></EditorName></Editor><Editor AffiliationIDS="Aff2"><EditorName DisplayOrder="Western"><GivenName>Takeo</GivenName><FamilyName>Kanade</FamilyName></EditorName></Editor><Editor AffiliationIDS="Aff3"><EditorName DisplayOrder="Western"><GivenName>Josef</GivenName><FamilyName>Kittler</FamilyName></EditorName></Editor><Editor AffiliationIDS="Aff4"><EditorName DisplayOrder="Western"><GivenName>Jon</GivenName><GivenName>M.</GivenName><FamilyName>Kleinberg</FamilyName></EditorName></Editor><Editor AffiliationIDS="Aff5"><EditorName 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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>978-3-642-13182-0</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="Chap31" Language="En"><ChapterInfo ChapterType="OriginalPaper" ContainsESM="No" NumberingDepth="2" NumberingStyle="ContentOnly" TocLevels="0"><ChapterID>31</ChapterID><ChapterDOI>10.1007/978-3-642-13182-0_31</ChapterDOI><ChapterSequenceNumber>31</ChapterSequenceNumber><ChapterTitle Language="En">A Faster Exact Algorithm for the Directed Maximum Leaf Spanning Tree Problem</ChapterTitle><ChapterFirstPage>328</ChapterFirstPage><ChapterLastPage>339</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>Daniel</GivenName><FamilyName>Binkele-Raible</FamilyName></AuthorName><Contact><Email>raible@informatik.uni-trier.de</Email></Contact></Author><Author AffiliationIDS="Aff18"><AuthorName DisplayOrder="Western"><GivenName>Henning</GivenName><FamilyName>Fernau</FamilyName></AuthorName><Contact><Email>fernau@informatik.uni-trier.de</Email></Contact></Author><Affiliation ID="Aff18"><OrgName>Univ.Trier, FB 4—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>Given a directed graph <Emphasis Type="Italic">G</Emphasis> = (<Emphasis Type="Italic">V</Emphasis>,<Emphasis Type="Italic">A</Emphasis>), the <Emphasis Type="SmallCaps">Directed Maximum Leaf Spanning Tree</Emphasis> problem asks to compute a directed spanning tree with as many leaves as possible. By designing a branching algorithm analyzed with <Emphasis Type="Italic">Measure&Conquer</Emphasis>, we show that the problem can be solved in time <InlineEquation ID="IEq1"><InlineMediaObject><ImageObject FileRef="978-3-642-13182-0_31_Chapter_TeX2GIFIEq1.gif" Format="GIF" Color="BlackWhite" Type="Linedraw" Rendition="HTML"></ImageObject></InlineMediaObject><EquationSource Format="TEX">${\mathcal{O}}^*({1.9044}^n)$</EquationSource></InlineEquation> using polynomial space. Allowing exponential space, this run time upper bound can be lowered to <InlineEquation ID="IEq2"><InlineMediaObject><ImageObject FileRef="978-3-642-13182-0_31_Chapter_TeX2GIFIEq2.gif" Format="GIF" Color="BlackWhite" Type="Linedraw" Rendition="HTML"></ImageObject></InlineMediaObject><EquationSource Format="TEX">${\mathcal{O}}^*(1.8139^n)$</EquationSource></InlineEquation>.</Para></Abstract></ChapterHeader><NoBody></NoBody></Chapter></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>A Faster Exact Algorithm for the Directed Maximum Leaf Spanning Tree Problem</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>A Faster Exact Algorithm for the Directed Maximum Leaf Spanning Tree Problem</title></titleInfo><name type="personal"><namePart type="given">Daniel</namePart><namePart type="family">Binkele-Raible</namePart><affiliation>Univ.Trier, FB 4—Abteilung Informatik, 54286, Trier, Germany</affiliation><affiliation>E-mail: raible@informatik.uni-trier.de</affiliation><role><roleTerm type="text">author</roleTerm></role></name><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@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">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: Given a directed graph G = (V,A), the Directed Maximum Leaf Spanning Tree problem asks to compute a directed spanning tree with as many leaves as possible. By designing a branching algorithm analyzed with Measure&Conquer, we show that the problem can be solved in time ${\mathcal{O}}^*({1.9044}^n)$ using polynomial space. Allowing exponential space, this run time upper bound can be lowered to ${\mathcal{O}}^*(1.8139^n)$ .</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" 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 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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">2010</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, 2010</recordOrigin></recordInfo></relatedItem><identifier type="istex">92E8A85F6DE5A50D60C19FBA7ADF63DFAE8DB524</identifier><identifier type="DOI">10.1007/978-3-642-13182-0_31</identifier><identifier type="ChapterID">31</identifier><identifier type="ChapterID">Chap31</identifier><accessCondition 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