An Exact Algorithm for the Maximum Leaf Spanning Tree Problem
Identifieur interne : 001B29 ( Istex/Corpus ); précédent : 001B28; suivant : 001B30An Exact Algorithm for the Maximum Leaf Spanning Tree Problem
Auteurs : Henning Fernau ; Joachim Kneis ; Dieter Kratsch ; Alexander Langer ; Mathieu Liedloff ; Daniel Raible ; Peter RossmanithSource :
- Lecture Notes in Computer Science [ 0302-9743 ] ; 2009.
Abstract
Abstract: Given an undirected graph G with n nodes, the Maximum Leaf Spanning Tree problem asks to find a spanning tree of G with as many leaves as possible. When parameterized in the number of leaves k, this problem can be solved in time O(4 k poly(n)) using a simple branching algorithm introduced by a subset of the authors [13]. Daligault, Gutin, Kim, and Yeo [6] improved this branching algorithm and obtained a running time of O(3.72 k poly(n)). In this paper, we study the problem from an exact exponential time point of view, where it is equivalent to the Connected Dominating Set problem. For this problem Fomin, Grandoni, and Kratsch showed how to break the Ω(2 n ) barrier and proposed an O(1.9407 n ) time algorithm [10]. Based on some properties of [6] and [13], we establish a branching algorithm whose running time of O(1.8966 n ) has been analyzed using the Measure-and-Conquer technique. Finally we provide a lower bound of Ω(1.4422 n ) for the worst case running time of our algorithm.
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DOI: 10.1007/978-3-642-11269-0_13
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Metz, 57045, Metz Cedex 01, France</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: kratsch@univ-metz.fr</mods:affiliation></affiliation></author><author><name sortKey="Langer, Alexander" sort="Langer, Alexander" uniqKey="Langer A" first="Alexander" last="Langer">Alexander Langer</name><affiliation><mods:affiliation>Department of Computer Science, RWTH Aachen University, Germany</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: langer@cs.rwth-aachen.de</mods:affiliation></affiliation></author><author><name sortKey="Liedloff, Mathieu" sort="Liedloff, Mathieu" uniqKey="Liedloff M" first="Mathieu" last="Liedloff">Mathieu Liedloff</name><affiliation><mods:affiliation>Laboratoire d’Informatique Fondamentale d’Orléans, Université d’Orléans, 45067, Orléans Cedex 2, France</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: liedloff@univ-orleans.fr</mods:affiliation></affiliation></author><author><name sortKey="Raible, Daniel" sort="Raible, Daniel" uniqKey="Raible D" first="Daniel" last="Raible">Daniel Raible</name><affiliation><mods:affiliation>Universität Trier, FB 4—Abteilung Informatik, D-54286, Trier, Germany</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: raible@uni-trier.de</mods:affiliation></affiliation></author><author><name sortKey="Rossmanith, Peter" sort="Rossmanith, Peter" uniqKey="Rossmanith P" first="Peter" last="Rossmanith">Peter Rossmanith</name><affiliation><mods:affiliation>Department of Computer Science, RWTH Aachen University, Germany</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: rossmani@cs.rwth-aachen.de</mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="s">Lecture Notes in Computer Science</title><imprint><date>2009</date></imprint><idno type="ISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="ISSN">0302-9743</idno></series><idno type="istex">7BE882E22D197384808B21F7979B89C0EB50025F</idno><idno type="DOI">10.1007/978-3-642-11269-0_13</idno><idno type="ChapterID">13</idno><idno type="ChapterID">Chap13</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0302-9743</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: Given an undirected graph G with n nodes, the Maximum Leaf Spanning Tree problem asks to find a spanning tree of G with as many leaves as possible. When parameterized in the number of leaves k, this problem can be solved in time O(4 k poly(n)) using a simple branching algorithm introduced by a subset of the authors [13]. Daligault, Gutin, Kim, and Yeo [6] improved this branching algorithm and obtained a running time of O(3.72 k poly(n)). In this paper, we study the problem from an exact exponential time point of view, where it is equivalent to the Connected Dominating Set problem. For this problem Fomin, Grandoni, and Kratsch showed how to break the Ω(2 n ) barrier and proposed an O(1.9407 n ) time algorithm [10]. Based on some properties of [6] and [13], we establish a branching algorithm whose running time of O(1.8966 n ) has been analyzed using the Measure-and-Conquer technique. Finally we provide a lower bound of Ω(1.4422 n ) for the worst case running time of our algorithm.</div></front></TEI><istex><corpusName>springer</corpusName><author><json:item><name>Henning Fernau</name><affiliations><json:string>Universität Trier, FB 4—Abteilung Informatik, D-54286, Trier, Germany</json:string><json:string>E-mail: fernau@uni-trier.de</json:string></affiliations></json:item><json:item><name>Joachim Kneis</name><affiliations><json:string>Department of Computer Science, RWTH Aachen University, Germany</json:string><json:string>E-mail: kneis@cs.rwth-aachen.de</json:string></affiliations></json:item><json:item><name>Dieter Kratsch</name><affiliations><json:string>Laboratoire d’Informatique Théorique et Appliquée, Université Paul Verlaine - Metz, 57045, Metz Cedex 01, France</json:string><json:string>E-mail: kratsch@univ-metz.fr</json:string></affiliations></json:item><json:item><name>Alexander Langer</name><affiliations><json:string>Department of Computer Science, RWTH Aachen University, Germany</json:string><json:string>E-mail: langer@cs.rwth-aachen.de</json:string></affiliations></json:item><json:item><name>Mathieu Liedloff</name><affiliations><json:string>Laboratoire d’Informatique Fondamentale d’Orléans, Université d’Orléans, 45067, Orléans Cedex 2, France</json:string><json:string>E-mail: liedloff@univ-orleans.fr</json:string></affiliations></json:item><json:item><name>Daniel Raible</name><affiliations><json:string>Universität Trier, FB 4—Abteilung Informatik, D-54286, Trier, Germany</json:string><json:string>E-mail: raible@uni-trier.de</json:string></affiliations></json:item><json:item><name>Peter Rossmanith</name><affiliations><json:string>Department of Computer Science, RWTH Aachen University, Germany</json:string><json:string>E-mail: rossmani@cs.rwth-aachen.de</json:string></affiliations></json:item></author><language><json:string>eng</json:string></language><originalGenre><json:string>OriginalPaper</json:string></originalGenre><abstract>Abstract: Given an undirected graph G with n nodes, the Maximum Leaf Spanning Tree problem asks to find a spanning tree of G with as many leaves as possible. When parameterized in the number of leaves k, this problem can be solved in time O(4 k poly(n)) using a simple branching algorithm introduced by a subset of the authors [13]. Daligault, Gutin, Kim, and Yeo [6] improved this branching algorithm and obtained a running time of O(3.72 k poly(n)). In this paper, we study the problem from an exact exponential time point of view, where it is equivalent to the Connected Dominating Set problem. For this problem Fomin, Grandoni, and Kratsch showed how to break the Ω(2 n ) barrier and proposed an O(1.9407 n ) time algorithm [10]. Based on some properties of [6] and [13], we establish a branching algorithm whose running time of O(1.8966 n ) has been analyzed using the Measure-and-Conquer technique. Finally we provide a lower bound of Ω(1.4422 n ) for the worst case running time of our algorithm.</abstract><qualityIndicators><score>8.552</score><pdfVersion>1.6</pdfVersion><pdfPageSize>430 x 660 pts</pdfPageSize><refBibsNative>false</refBibsNative><keywordCount>0</keywordCount><abstractCharCount>1003</abstractCharCount><pdfWordCount>5658</pdfWordCount><pdfCharCount>24551</pdfCharCount><pdfPageCount>12</pdfPageCount><abstractWordCount>171</abstractWordCount></qualityIndicators><title>An Exact Algorithm for the Maximum Leaf Spanning Tree Problem</title><chapterId><json:string>13</json:string><json:string>Chap13</json:string></chapterId><refBibs><json:item><author><json:item><name>H,L Bodlaender</name></json:item></author><host><volume>14</volume><pages><last>23</last><first>1</first></pages><issue>1</issue><author></author><title>J. 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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>2009</copyrightDate></serie><host><editor><json:item><name>Jianer Chen</name><affiliations><json:string>Department of Computer Science and Engineering, Texas A&M University, College Station, 77843, Texas, USA</json:string><json:string>E-mail: chen@cs.tamu.edu</json:string></affiliations></json:item><json:item><name>Fedor V. Fomin</name><affiliations><json:string>Institutt for informatikk, Universitetet i Bergen, Postboks 7803, 5020, Bergen, Norway</json:string><json:string>E-mail: Fomin@ii.uib.no</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>Algorithms</value></json:item><json:item><value>Discrete Mathematics in Computer Science</value></json:item><json:item><value>Theory of Computation</value></json:item><json:item><value>Symbolic and Algebraic Manipulation</value></json:item><json:item><value>Logics and Meanings of Programs</value></json:item></subject><isbn><json:string>978-3-642-11268-3</json:string></isbn><language><json:string>unknown</json:string></language><eissn><json:string>1611-3349</json:string></eissn><title>Parameterized and Exact Computation</title><bookId><json:string>978-3-642-11269-0</json:string></bookId><volume>5917</volume><pages><last>172</last><first>161</first></pages><issn><json:string>0302-9743</json:string></issn><genre><json:string>book-series</json:string></genre><eisbn><json:string>978-3-642-11269-0</json:string></eisbn><copyrightDate>2009</copyrightDate><doi><json:string>10.1007/978-3-642-11269-0</json:string></doi></host><publicationDate>2009</publicationDate><copyrightDate>2009</copyrightDate><doi><json:string>10.1007/978-3-642-11269-0_13</json:string></doi><id>7BE882E22D197384808B21F7979B89C0EB50025F</id><score>0.32894838</score><fulltext><json:item><extension>pdf</extension><original>true</original><mimetype>application/pdf</mimetype><uri>https://api.istex.fr/document/7BE882E22D197384808B21F7979B89C0EB50025F/fulltext/pdf</uri></json:item><json:item><extension>zip</extension><original>false</original><mimetype>application/zip</mimetype><uri>https://api.istex.fr/document/7BE882E22D197384808B21F7979B89C0EB50025F/fulltext/zip</uri></json:item><istex:fulltextTEI uri="https://api.istex.fr/document/7BE882E22D197384808B21F7979B89C0EB50025F/fulltext/tei"><teiHeader><fileDesc><titleStmt><title level="a" type="main" xml:lang="en">An Exact Algorithm for the Maximum Leaf Spanning Tree Problem</title><respStmt><resp>Références bibliographiques récupérées via GROBID</resp><name resp="ISTEX-API">ISTEX-API (INIST-CNRS)</name></respStmt><respStmt><resp>Références bibliographiques récupérées via GROBID</resp><name resp="ISTEX-API">ISTEX-API (INIST-CNRS)</name></respStmt></titleStmt><publicationStmt><authority>ISTEX</authority><publisher>Springer Berlin Heidelberg</publisher><pubPlace>Berlin, Heidelberg</pubPlace><availability><p>Springer-Verlag Berlin Heidelberg, 2009</p></availability><date>2009</date></publicationStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a" type="main" xml:lang="en">An Exact Algorithm for the Maximum Leaf Spanning Tree Problem</title><author xml:id="author-1"><persName><forename type="first">Henning</forename><surname>Fernau</surname></persName><email>fernau@uni-trier.de</email><affiliation>Universität Trier, FB 4—Abteilung Informatik, D-54286, Trier, Germany</affiliation></author><author xml:id="author-2"><persName><forename type="first">Joachim</forename><surname>Kneis</surname></persName><email>kneis@cs.rwth-aachen.de</email><affiliation>Department of Computer Science, RWTH Aachen University, Germany</affiliation></author><author xml:id="author-3"><persName><forename type="first">Dieter</forename><surname>Kratsch</surname></persName><email>kratsch@univ-metz.fr</email><affiliation>Laboratoire d’Informatique Théorique et Appliquée, Université Paul Verlaine - Metz, 57045, Metz Cedex 01, France</affiliation></author><author xml:id="author-4"><persName><forename type="first">Alexander</forename><surname>Langer</surname></persName><email>langer@cs.rwth-aachen.de</email><affiliation>Department of Computer Science, RWTH Aachen University, Germany</affiliation></author><author xml:id="author-5"><persName><forename type="first">Mathieu</forename><surname>Liedloff</surname></persName><email>liedloff@univ-orleans.fr</email><affiliation>Laboratoire d’Informatique Fondamentale d’Orléans, Université d’Orléans, 45067, Orléans Cedex 2, France</affiliation></author><author xml:id="author-6"><persName><forename type="first">Daniel</forename><surname>Raible</surname></persName><email>raible@uni-trier.de</email><affiliation>Universität Trier, FB 4—Abteilung Informatik, D-54286, Trier, Germany</affiliation></author><author xml:id="author-7"><persName><forename type="first">Peter</forename><surname>Rossmanith</surname></persName><email>rossmani@cs.rwth-aachen.de</email><affiliation>Department of Computer Science, RWTH Aachen University, Germany</affiliation></author></analytic><monogr><title level="m">Parameterized and Exact Computation</title><title level="m" type="sub">4th International Workshop, IWPEC 2009, Copenhagen, Denmark, September 10-11, 2009, Revised Selected Papers</title><idno type="pISBN">978-3-642-11268-3</idno><idno type="eISBN">978-3-642-11269-0</idno><idno type="pISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="DOI">10.1007/978-3-642-11269-0</idno><idno type="book-ID">978-3-642-11269-0</idno><idno type="book-title-ID">194112</idno><idno type="book-sequence-number">5917</idno><idno type="book-volume-number">5917</idno><idno type="book-chapter-count">27</idno><editor><persName><forename type="first">Jianer</forename><surname>Chen</surname></persName><email>chen@cs.tamu.edu</email><affiliation>Department of Computer Science and Engineering, Texas A&M University, College Station, 77843, Texas, USA</affiliation></editor><editor><persName><forename type="first">Fedor</forename><forename type="first">V.</forename><surname>Fomin</surname></persName><email>Fomin@ii.uib.no</email><affiliation>Institutt for informatikk, Universitetet i Bergen, Postboks 7803, 5020, Bergen, Norway</affiliation></editor><imprint><publisher>Springer Berlin Heidelberg</publisher><pubPlace>Berlin, Heidelberg</pubPlace><date type="published" when="2009"></date><biblScope unit="volume">5917</biblScope><biblScope unit="page" from="161">161</biblScope><biblScope unit="page" to="172">172</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>2009</date></biblScope><idno type="pISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="series-Id">558</idno></series><idno type="istex">7BE882E22D197384808B21F7979B89C0EB50025F</idno><idno type="DOI">10.1007/978-3-642-11269-0_13</idno><idno type="ChapterID">13</idno><idno type="ChapterID">Chap13</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>2009</date></creation><langUsage><language ident="en">en</language></langUsage><abstract xml:lang="en"><p>Abstract: Given an undirected graph G with n nodes, the Maximum Leaf Spanning Tree problem asks to find a spanning tree of G with as many leaves as possible. When parameterized in the number of leaves k, this problem can be solved in time O(4 k poly(n)) using a simple branching algorithm introduced by a subset of the authors [13]. Daligault, Gutin, Kim, and Yeo [6] improved this branching algorithm and obtained a running time of O(3.72 k poly(n)). In this paper, we study the problem from an exact exponential time point of view, where it is equivalent to the Connected Dominating Set problem. For this problem Fomin, Grandoni, and Kratsch showed how to break the Ω(2 n ) barrier and proposed an O(1.9407 n ) time algorithm [10]. Based on some properties of [6] and [13], we establish a branching algorithm whose running time of O(1.8966 n ) has been analyzed using the Measure-and-Conquer technique. Finally we provide a lower bound of Ω(1.4422 n ) for the worst case running time of our algorithm.</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>M14018</label><label>I17028</label><label>I16005</label><label>I17052</label><label>I1603X</label><item><term>Computer Science</term></item><item><term>Algorithm Analysis and Problem Complexity</term></item><item><term>Algorithms</term></item><item><term>Discrete Mathematics in Computer Science</term></item><item><term>Theory of Computation</term></item><item><term>Symbolic and Algebraic Manipulation</term></item><item><term>Logics and Meanings of Programs</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="2009">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/7BE882E22D197384808B21F7979B89C0EB50025F/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 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" NumberingStyle="ContentOnly" OutputMedium="All" TocLevels="0"><BookID>978-3-642-11269-0</BookID><BookTitle>Parameterized and Exact Computation</BookTitle><BookSubTitle>4th International Workshop, IWPEC 2009, Copenhagen, Denmark, September 10-11, 2009, Revised Selected Papers</BookSubTitle><BookVolumeNumber>5917</BookVolumeNumber><BookSequenceNumber>5917</BookSequenceNumber><BookDOI>10.1007/978-3-642-11269-0</BookDOI><BookTitleID>194112</BookTitleID><BookPrintISBN>978-3-642-11268-3</BookPrintISBN><BookElectronicISBN>978-3-642-11269-0</BookElectronicISBN><BookChapterCount>27</BookChapterCount><BookCopyright><CopyrightHolderName>Springer-Verlag Berlin Heidelberg</CopyrightHolderName><CopyrightYear>2009</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="M14018" Priority="2" Type="Secondary">Algorithms</BookSubject><BookSubject Code="I17028" Priority="3" Type="Secondary">Discrete Mathematics in Computer Science</BookSubject><BookSubject Code="I16005" Priority="4" Type="Secondary">Theory of Computation</BookSubject><BookSubject Code="I17052" Priority="5" Type="Secondary">Symbolic and Algebraic Manipulation</BookSubject><BookSubject Code="I1603X" Priority="6" Type="Secondary">Logics and Meanings of Programs</BookSubject><SubjectCollection Code="SUCO11645">Computer Science</SubjectCollection></BookSubjectGroup><BookContext><SeriesID>558</SeriesID></BookContext></BookInfo><BookHeader><EditorGroup><Editor AffiliationIDS="Aff16"><EditorName DisplayOrder="Western"><GivenName>Jianer</GivenName><FamilyName>Chen</FamilyName></EditorName><Contact><Email>chen@cs.tamu.edu</Email></Contact></Editor><Editor AffiliationIDS="Aff17"><EditorName DisplayOrder="Western"><GivenName>Fedor</GivenName><GivenName>V.</GivenName><FamilyName>Fomin</FamilyName></EditorName><Contact><Email>Fomin@ii.uib.no</Email></Contact></Editor><Affiliation ID="Aff16"><OrgDivision>Department of Computer Science and Engineering</OrgDivision><OrgName>Texas A&M University</OrgName><OrgAddress><Street>College Station</Street><Postcode>77843</Postcode><City>Texas</City><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff17"><OrgDivision>Institutt for informatikk</OrgDivision><OrgName>Universitetet i Bergen</OrgName><OrgAddress><Postbox>Postboks 7803</Postbox><Postcode>5020</Postcode><City>Bergen</City><Country>Norway</Country></OrgAddress></Affiliation></EditorGroup></BookHeader><Chapter ID="Chap13" Language="En"><ChapterInfo ChapterType="OriginalPaper" ContainsESM="No" NumberingStyle="ContentOnly" TocLevels="0"><ChapterID>13</ChapterID><ChapterDOI>10.1007/978-3-642-11269-0_13</ChapterDOI><ChapterSequenceNumber>13</ChapterSequenceNumber><ChapterTitle Language="En">An Exact Algorithm for the Maximum Leaf Spanning Tree Problem</ChapterTitle><ChapterFirstPage>161</ChapterFirstPage><ChapterLastPage>172</ChapterLastPage><ChapterCopyright><CopyrightHolderName>Springer-Verlag Berlin Heidelberg</CopyrightHolderName><CopyrightYear>2009</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>978-3-642-11269-0</BookID><BookTitle>Parameterized and Exact Computation</BookTitle></ChapterContext></ChapterInfo><ChapterHeader><AuthorGroup><Author AffiliationIDS="Aff18"><AuthorName DisplayOrder="Western"><GivenName>Henning</GivenName><FamilyName>Fernau</FamilyName></AuthorName><Contact><Email>fernau@uni-trier.de</Email></Contact></Author><Author AffiliationIDS="Aff19"><AuthorName DisplayOrder="Western"><GivenName>Joachim</GivenName><FamilyName>Kneis</FamilyName></AuthorName><Contact><Email>kneis@cs.rwth-aachen.de</Email></Contact></Author><Author AffiliationIDS="Aff20"><AuthorName DisplayOrder="Western"><GivenName>Dieter</GivenName><FamilyName>Kratsch</FamilyName></AuthorName><Contact><Email>kratsch@univ-metz.fr</Email></Contact></Author><Author AffiliationIDS="Aff19"><AuthorName DisplayOrder="Western"><GivenName>Alexander</GivenName><FamilyName>Langer</FamilyName></AuthorName><Contact><Email>langer@cs.rwth-aachen.de</Email></Contact></Author><Author AffiliationIDS="Aff21"><AuthorName DisplayOrder="Western"><GivenName>Mathieu</GivenName><FamilyName>Liedloff</FamilyName></AuthorName><Contact><Email>liedloff@univ-orleans.fr</Email></Contact></Author><Author AffiliationIDS="Aff18"><AuthorName DisplayOrder="Western"><GivenName>Daniel</GivenName><FamilyName>Raible</FamilyName></AuthorName><Contact><Email>raible@uni-trier.de</Email></Contact></Author><Author AffiliationIDS="Aff19"><AuthorName DisplayOrder="Western"><GivenName>Peter</GivenName><FamilyName>Rossmanith</FamilyName></AuthorName><Contact><Email>rossmani@cs.rwth-aachen.de</Email></Contact></Author><Affiliation ID="Aff18"><OrgName>Universität Trier</OrgName><OrgAddress><Street>FB 4—Abteilung Informatik</Street><Postcode>D-54286</Postcode><City>Trier</City><Country>Germany</Country></OrgAddress></Affiliation><Affiliation ID="Aff19"><OrgDivision>Department of Computer Science</OrgDivision><OrgName>RWTH Aachen University</OrgName><OrgAddress><Country>Germany</Country></OrgAddress></Affiliation><Affiliation ID="Aff20"><OrgDivision>Laboratoire d’Informatique Théorique et Appliquée</OrgDivision><OrgName>Université Paul Verlaine - Metz</OrgName><OrgAddress><Postcode>57045</Postcode><City>Metz Cedex 01</City><Country>France</Country></OrgAddress></Affiliation><Affiliation ID="Aff21"><OrgDivision>Laboratoire d’Informatique Fondamentale d’Orléans</OrgDivision><OrgName>Université d’Orléans</OrgName><OrgAddress><Postcode>45067</Postcode><City>Orléans Cedex 2</City><Country>France</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>Given an undirected graph <Emphasis Type="Italic">G</Emphasis> with <Emphasis Type="Italic">n</Emphasis> nodes, the Maximum Leaf Spanning Tree problem asks to find a spanning tree of <Emphasis Type="Italic">G</Emphasis> with as many leaves as possible. When parameterized in the number of leaves <Emphasis Type="Italic">k</Emphasis>, this problem can be solved in time <Emphasis Type="Italic">O</Emphasis>(4<Superscript><Emphasis Type="Italic">k</Emphasis></Superscript>poly(<Emphasis Type="Italic">n</Emphasis>)) using a simple branching algorithm introduced by a subset of the authors [13]. Daligault, Gutin, Kim, and Yeo [6] improved this branching algorithm and obtained a running time of <Emphasis Type="Italic">O</Emphasis>(3.72<Superscript><Emphasis Type="Italic">k</Emphasis></Superscript>poly(<Emphasis Type="Italic">n</Emphasis>)). In this paper, we study the problem from an exact exponential time point of view, where it is equivalent to the Connected Dominating Set problem. For this problem Fomin, Grandoni, and Kratsch showed how to break the Ω(2<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>) barrier and proposed an <Emphasis Type="Italic">O</Emphasis>(1.9407<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>) time algorithm [10]. Based on some properties of [6] and [13], we establish a branching algorithm whose running time of <Emphasis Type="Italic">O</Emphasis>(1.8966<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>) has been analyzed using the Measure-and-Conquer technique. Finally we provide a lower bound of Ω(1.4422<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>) for the worst case running time of our algorithm.</Para></Abstract></ChapterHeader><NoBody></NoBody></Chapter></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>An Exact Algorithm for the Maximum Leaf Spanning Tree Problem</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>An Exact Algorithm for the Maximum Leaf Spanning Tree Problem</title></titleInfo><name type="personal"><namePart type="given">Henning</namePart><namePart type="family">Fernau</namePart><affiliation>Universität Trier, FB 4—Abteilung Informatik, D-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">Joachim</namePart><namePart type="family">Kneis</namePart><affiliation>Department of Computer Science, RWTH Aachen University, Germany</affiliation><affiliation>E-mail: kneis@cs.rwth-aachen.de</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Dieter</namePart><namePart type="family">Kratsch</namePart><affiliation>Laboratoire d’Informatique Théorique et Appliquée, Université Paul Verlaine - Metz, 57045, Metz Cedex 01, France</affiliation><affiliation>E-mail: kratsch@univ-metz.fr</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Alexander</namePart><namePart type="family">Langer</namePart><affiliation>Department of Computer Science, RWTH Aachen University, Germany</affiliation><affiliation>E-mail: langer@cs.rwth-aachen.de</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Mathieu</namePart><namePart type="family">Liedloff</namePart><affiliation>Laboratoire d’Informatique Fondamentale d’Orléans, Université d’Orléans, 45067, Orléans Cedex 2, France</affiliation><affiliation>E-mail: liedloff@univ-orleans.fr</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 4—Abteilung Informatik, D-54286, Trier, Germany</affiliation><affiliation>E-mail: raible@uni-trier.de</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Peter</namePart><namePart type="family">Rossmanith</namePart><affiliation>Department of Computer Science, RWTH Aachen University, Germany</affiliation><affiliation>E-mail: rossmani@cs.rwth-aachen.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">2009</dateIssued><copyrightDate encoding="w3cdtf">2009</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 an undirected graph G with n nodes, the Maximum Leaf Spanning Tree problem asks to find a spanning tree of G with as many leaves as possible. When parameterized in the number of leaves k, this problem can be solved in time O(4 k poly(n)) using a simple branching algorithm introduced by a subset of the authors [13]. Daligault, Gutin, Kim, and Yeo [6] improved this branching algorithm and obtained a running time of O(3.72 k poly(n)). In this paper, we study the problem from an exact exponential time point of view, where it is equivalent to the Connected Dominating Set problem. For this problem Fomin, Grandoni, and Kratsch showed how to break the Ω(2 n ) barrier and proposed an O(1.9407 n ) time algorithm [10]. Based on some properties of [6] and [13], we establish a branching algorithm whose running time of O(1.8966 n ) has been analyzed using the Measure-and-Conquer technique. Finally we provide a lower bound of Ω(1.4422 n ) for the worst case running time of our algorithm.</abstract><relatedItem type="host"><titleInfo><title>Parameterized and Exact Computation</title><subTitle>4th International Workshop, IWPEC 2009, Copenhagen, Denmark, September 10-11, 2009, Revised Selected Papers</subTitle></titleInfo><name type="personal"><namePart type="given">Jianer</namePart><namePart type="family">Chen</namePart><affiliation>Department of Computer Science and Engineering, Texas A&M University, College Station, 77843, Texas, USA</affiliation><affiliation>E-mail: chen@cs.tamu.edu</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Fedor</namePart><namePart type="given">V.</namePart><namePart type="family">Fomin</namePart><affiliation>Institutt for informatikk, Universitetet i Bergen, Postboks 7803, 5020, Bergen, Norway</affiliation><affiliation>E-mail: Fomin@ii.uib.no</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><genre type="book-series" displayLabel="Proceedings"></genre><originInfo><copyrightDate encoding="w3cdtf">2009</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="M14018">Algorithms</topic><topic authority="SpringerSubjectCodes" authorityURI="I17028">Discrete Mathematics in Computer Science</topic><topic authority="SpringerSubjectCodes" authorityURI="I16005">Theory of Computation</topic><topic authority="SpringerSubjectCodes" authorityURI="I17052">Symbolic and Algebraic Manipulation</topic><topic authority="SpringerSubjectCodes" authorityURI="I1603X">Logics and Meanings of Programs</topic></subject><identifier type="DOI">10.1007/978-3-642-11269-0</identifier><identifier type="ISBN">978-3-642-11268-3</identifier><identifier type="eISBN">978-3-642-11269-0</identifier><identifier type="ISSN">0302-9743</identifier><identifier type="eISSN">1611-3349</identifier><identifier type="BookTitleID">194112</identifier><identifier type="BookID">978-3-642-11269-0</identifier><identifier type="BookChapterCount">27</identifier><identifier type="BookVolumeNumber">5917</identifier><identifier type="BookSequenceNumber">5917</identifier><part><date>2009</date><detail type="volume"><number>5917</number><caption>vol.</caption></detail><extent unit="pages"><start>161</start><end>172</end></extent></part><recordInfo><recordOrigin>Springer-Verlag Berlin Heidelberg, 2009</recordOrigin></recordInfo></relatedItem><relatedItem type="series"><titleInfo><title>Lecture Notes in Computer Science</title></titleInfo><name type="personal"><namePart type="given">David</namePart><namePart 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 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">2009</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, 2009</recordOrigin></recordInfo></relatedItem><identifier type="istex">7BE882E22D197384808B21F7979B89C0EB50025F</identifier><identifier type="DOI">10.1007/978-3-642-11269-0_13</identifier><identifier type="ChapterID">13</identifier><identifier type="ChapterID">Chap13</identifier><accessCondition type="use and reproduction" contentType="copyright">Springer-Verlag Berlin Heidelberg, 2009</accessCondition><recordInfo><recordContentSource>SPRINGER</recordContentSource><recordOrigin>Springer-Verlag Berlin Heidelberg, 2009</recordOrigin></recordInfo></mods></metadata></istex></record>Pour manipuler ce document sous Unix (Dilib)
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