A Parameterized Route to Exact Puzzles: Breaking the 2 n -Barrier for Irredundance
Identifieur interne : 001B33 ( Istex/Corpus ); précédent : 001B32; suivant : 001B34A Parameterized Route to Exact Puzzles: Breaking the 2 n -Barrier for Irredundance
Auteurs : Daniel Binkele-Raible ; Ljiljana Brankovic ; Henning Fernau ; Joachim Kneis ; Dieter Kratsch ; Alexander Langer ; Mathieu Liedloff ; Peter RossmanithSource :
- Lecture Notes in Computer Science [ 0302-9743 ] ; 2010.
Abstract
Abstract: The lower and the upper irredundance numbers of a graph G, denoted ir(G) and IR(G) respectively, are conceptually linked to domination and independence numbers and have numerous relations to other graph parameters. It is a long-standing open question whether determining these numbers for a graph G on n vertices admits exact algorithms running in time less than the trivial Ω(2 n ) enumeration barrier. We solve this open problem by devising parameterized algorithms for the duals of the natural parameterizations of the problems with running times faster than $\mathcal{O}^*(4^{k})$ . For example, we present an algorithm running in time $\mathcal{O}^*(3.069^{k}))$ for determining whether IR(G) is at least n − k. Although the corresponding problem has been shown to be in FPT by kernelization techniques, this paper offers the first parameterized algorithms with an exponential dependency on the parameter in the running time. Furthermore, these seem to be the first examples of a parameterized approach leading to a solution to a problem in exponential time algorithmics where the natural interpretation as exact exponential-time algorithms fails.
Url:
DOI: 10.1007/978-3-642-13073-1_28
Links to Exploration step
ISTEX:D53E1C54122748DE8921D66B3B2ABDDBDB118DD2Le document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">A Parameterized Route to Exact Puzzles: Breaking the 2 n -Barrier for Irredundance</title><author><name sortKey="Binkele Raible, Daniel" sort="Binkele Raible, Daniel" uniqKey="Binkele Raible D" first="Daniel" last="Binkele-Raible">Daniel Binkele-Raible</name><affiliation><mods:affiliation>FB 4—Abteilung Informatik, Universität Trier, D-54286, Trier, Germany</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: fernau@uni-trier.de</mods:affiliation></affiliation></author><author><name sortKey="Brankovic, Ljiljana" sort="Brankovic, Ljiljana" uniqKey="Brankovic L" first="Ljiljana" last="Brankovic">Ljiljana Brankovic</name><affiliation><mods:affiliation>The University of Newcastle, University Drive, NSW 2308, Callaghan, Australia</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: ljiljana.brankovic@newcastle.edu.au</mods:affiliation></affiliation></author><author><name sortKey="Fernau, Henning" sort="Fernau, Henning" uniqKey="Fernau H" first="Henning" last="Fernau">Henning Fernau</name><affiliation><mods:affiliation>FB 4—Abteilung Informatik, Universität Trier, D-54286, Trier, Germany</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: raible@uni-trier.de</mods:affiliation></affiliation></author><author><name sortKey="Kneis, Joachim" sort="Kneis, Joachim" uniqKey="Kneis J" first="Joachim" last="Kneis">Joachim Kneis</name><affiliation><mods:affiliation>Department of Computer Science, RWTH Aachen University, Germany</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: kneis@cs.rwth-aachen.de</mods:affiliation></affiliation></author><author><name sortKey="Kratsch, Dieter" sort="Kratsch, Dieter" uniqKey="Kratsch D" first="Dieter" last="Kratsch">Dieter Kratsch</name><affiliation><mods:affiliation>Laboratoire d’Informatique Théorique et Appliquée, Université Paul Verlaine - 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="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></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:D53E1C54122748DE8921D66B3B2ABDDBDB118DD2</idno><date when="2010" year="2010">2010</date><idno type="doi">10.1007/978-3-642-13073-1_28</idno><idno type="url">https://api.istex.fr/document/D53E1C54122748DE8921D66B3B2ABDDBDB118DD2/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">001B33</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">001B33</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">A Parameterized Route to Exact Puzzles: Breaking the 2 n -Barrier for Irredundance</title><author><name sortKey="Binkele Raible, Daniel" sort="Binkele Raible, Daniel" uniqKey="Binkele Raible D" first="Daniel" last="Binkele-Raible">Daniel Binkele-Raible</name><affiliation><mods:affiliation>FB 4—Abteilung Informatik, Universität Trier, D-54286, Trier, Germany</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: fernau@uni-trier.de</mods:affiliation></affiliation></author><author><name sortKey="Brankovic, Ljiljana" sort="Brankovic, Ljiljana" uniqKey="Brankovic L" first="Ljiljana" last="Brankovic">Ljiljana Brankovic</name><affiliation><mods:affiliation>The University of Newcastle, University Drive, NSW 2308, Callaghan, Australia</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: ljiljana.brankovic@newcastle.edu.au</mods:affiliation></affiliation></author><author><name sortKey="Fernau, Henning" sort="Fernau, Henning" uniqKey="Fernau H" first="Henning" last="Fernau">Henning Fernau</name><affiliation><mods:affiliation>FB 4—Abteilung Informatik, Universität Trier, D-54286, Trier, Germany</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: raible@uni-trier.de</mods:affiliation></affiliation></author><author><name sortKey="Kneis, Joachim" sort="Kneis, Joachim" uniqKey="Kneis J" first="Joachim" last="Kneis">Joachim Kneis</name><affiliation><mods:affiliation>Department of Computer Science, RWTH Aachen University, Germany</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: kneis@cs.rwth-aachen.de</mods:affiliation></affiliation></author><author><name sortKey="Kratsch, Dieter" sort="Kratsch, Dieter" uniqKey="Kratsch D" first="Dieter" last="Kratsch">Dieter Kratsch</name><affiliation><mods:affiliation>Laboratoire d’Informatique Théorique et Appliquée, Université Paul Verlaine - 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="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>2010</date></imprint><idno type="ISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="ISSN">0302-9743</idno></series><idno type="istex">D53E1C54122748DE8921D66B3B2ABDDBDB118DD2</idno><idno type="DOI">10.1007/978-3-642-13073-1_28</idno><idno type="ChapterID">28</idno><idno type="ChapterID">Chap28</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: The lower and the upper irredundance numbers of a graph G, denoted ir(G) and IR(G) respectively, are conceptually linked to domination and independence numbers and have numerous relations to other graph parameters. It is a long-standing open question whether determining these numbers for a graph G on n vertices admits exact algorithms running in time less than the trivial Ω(2 n ) enumeration barrier. We solve this open problem by devising parameterized algorithms for the duals of the natural parameterizations of the problems with running times faster than $\mathcal{O}^*(4^{k})$ . For example, we present an algorithm running in time $\mathcal{O}^*(3.069^{k}))$ for determining whether IR(G) is at least n − k. Although the corresponding problem has been shown to be in FPT by kernelization techniques, this paper offers the first parameterized algorithms with an exponential dependency on the parameter in the running time. Furthermore, these seem to be the first examples of a parameterized approach leading to a solution to a problem in exponential time algorithmics where the natural interpretation as exact exponential-time algorithms fails.</div></front></TEI><istex><corpusName>springer</corpusName><author><json:item><name>Daniel Binkele-Raible</name><affiliations><json:string>FB 4—Abteilung Informatik, Universität Trier, D-54286, Trier, Germany</json:string><json:string>E-mail: fernau@uni-trier.de</json:string></affiliations></json:item><json:item><name>Ljiljana Brankovic</name><affiliations><json:string>The University of Newcastle, University Drive, NSW 2308, Callaghan, 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>FB 4—Abteilung Informatik, Universität Trier, D-54286, Trier, Germany</json:string><json:string>E-mail: raible@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>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: The lower and the upper irredundance numbers of a graph G, denoted ir(G) and IR(G) respectively, are conceptually linked to domination and independence numbers and have numerous relations to other graph parameters. It is a long-standing open question whether determining these numbers for a graph G on n vertices admits exact algorithms running in time less than the trivial Ω(2 n ) enumeration barrier. We solve this open problem by devising parameterized algorithms for the duals of the natural parameterizations of the problems with running times faster than $\mathcal{O}^*(4^{k})$ . For example, we present an algorithm running in time $\mathcal{O}^*(3.069^{k}))$ for determining whether IR(G) is at least n − k. Although the corresponding problem has been shown to be in FPT by kernelization techniques, this paper offers the first parameterized algorithms with an exponential dependency on the parameter in the running time. Furthermore, these seem to be the first examples of a parameterized approach leading to a solution to a problem in exponential time algorithmics where the natural interpretation as exact exponential-time algorithms fails.</abstract><qualityIndicators><score>8.564</score><pdfVersion>1.6</pdfVersion><pdfPageSize>430 x 660 pts</pdfPageSize><refBibsNative>false</refBibsNative><keywordCount>0</keywordCount><abstractCharCount>1162</abstractCharCount><pdfWordCount>6307</pdfWordCount><pdfCharCount>27678</pdfCharCount><pdfPageCount>12</pdfPageCount><abstractWordCount>172</abstractWordCount></qualityIndicators><title>A Parameterized Route to Exact Puzzles: Breaking the 2 n -Barrier for Irredundance</title><chapterId><json:string>28</json:string><json:string>Chap28</json:string></chapterId><refBibs><json:item><author><json:item><name>O Favaron</name></json:item><json:item><name>T,W Haynes</name></json:item><json:item><name>S,T Hedetniemi</name></json:item><json:item><name>M,A Henning</name></json:item><json:item><name>D,J Knisley</name></json:item></author><host><volume>256</volume><pages><last>127</last><first>115</first></pages><issue>12</issue><author></author><title>Discrete Mathematics</title><publicationDate>2002</publicationDate></host><title>Total irredundance in graphs</title><publicationDate>2002</publicationDate></json:item><json:item><author><json:item><name>R,B Allan</name></json:item><json:item><name>R Laskar</name></json:item></author><host><volume>23</volume><pages><last>76</last><first>73</first></pages><issue>2</issue><author></author><title>Discrete Mathematics</title><publicationDate>1978</publicationDate></host><title>On domination and independent domination numbers of a graph</title><publicationDate>1978</publicationDate></json:item><json:item><author><json:item><name>O Favaron</name></json:item></author><host><volume>70</volume><pages><last>20</last><first>17</first></pages><issue>1</issue><author></author><title>Discrete Mathematics</title><publicationDate>1988</publicationDate></host><title>Two relations between the parameters of independence and irredundance</title><publicationDate>1988</publicationDate></json:item><json:item><author><json:item><name>M,R Fellows</name></json:item><json:item><name>G Fricke</name></json:item><json:item><name>S,T Hedetniemi</name></json:item><json:item><name>D,P Jacobs</name></json:item></author><host><volume>7</volume><pages><last>47</last><first>41</first></pages><issue>1</issue><author></author><title>SIAM J. Discrete Math</title><publicationDate>1994</publicationDate></host><title>The private neighbor cube</title><publicationDate>1994</publicationDate></json:item><json:item><author><json:item><name>S,T Hedetniemi</name></json:item><json:item><name>R Laskar</name></json:item><json:item><name>J Pfaff</name></json:item></author><host><volume>48</volume><pages><last>193</last><first>183</first></pages><author></author><title>Congr. Numer</title><publicationDate>1985</publicationDate></host><title>Irredundance in graphs: a survey</title><publicationDate>1985</publicationDate></json:item><json:item><author><json:item><name>B Bollobás</name></json:item><json:item><name>E,J Cockayne</name></json:item></author><host><volume>3</volume><pages><last>250</last><first>241</first></pages><author></author><title>J. Graph Theory</title><publicationDate>1979</publicationDate></host><title>Graph-theoretic parameters concerning domination, independence, and irredundance</title><publicationDate>1979</publicationDate></json:item><json:item><author><json:item><name>E,J Cockayne</name></json:item><json:item><name>P,J P Grobler</name></json:item><json:item><name>S,T Hedetniemi</name></json:item><json:item><name>A,A Mcrae</name></json:item></author><host><volume>25</volume><pages><last>224</last><first>213</first></pages><author></author><title>J. Combin. Math. Combin. Comput</title><publicationDate>1997</publicationDate></host><title>What makes an irredundant set maximal?</title><publicationDate>1997</publicationDate></json:item><json:item><author><json:item><name>M,S Chang</name></json:item><json:item><name>P Nagavamsi</name></json:item><json:item><name>C,P Rangan</name></json:item></author><host><volume>66</volume><pages><last>70</last><first>65</first></pages><author></author><title>Information Processing Letters</title><publicationDate>1998</publicationDate></host><title>Weighted irredundance of interval graphs</title><publicationDate>1998</publicationDate></json:item><json:item><author><json:item><name>E,J Cockayne</name></json:item><json:item><name>S,T Hedetniemi</name></json:item><json:item><name>D,J Miller</name></json:item></author><host><volume>21</volume><pages><last>468</last><first>461</first></pages><issue>4</issue><author></author><title>Canad. Math. Bull</title><publicationDate>1978</publicationDate></host><title>Properties of hereditary hypergraphs and middle graphs</title><publicationDate>1978</publicationDate></json:item><json:item><author><json:item><name>T,W Haynes</name></json:item><json:item><name>S,T Hedetniemi</name></json:item><json:item><name>P,J Slater</name></json:item></author><host><author></author><title>Monographs and Textbooks in Pure and Applied Mathematics</title><publicationDate>1998</publicationDate></host><title>Fundamentals of Domination in Graphs</title><publicationDate>1998</publicationDate></json:item><json:item><author><json:item><name>C,J Colbourn</name></json:item><json:item><name>A Proskurowski</name></json:item></author><host><pages><last>136</last><first>128</first></pages><author></author><title>ICALP 1984</title><publicationDate>1984</publicationDate></host><title>Concurrent transmissions in broadcast networks</title><publicationDate>1984</publicationDate></json:item><json:item><host><author><json:item><name>R,G Downey</name></json:item><json:item><name>M,R Fellows</name></json:item></author><publicationDate>1999</publicationDate></host></json:item><json:item><author><json:item><name>V Raman</name></json:item><json:item><name>S Saurabh</name></json:item><json:item><name>R,G Downey</name></json:item><json:item><name>M,R Fellows</name></json:item><json:item><name>V Raman</name></json:item></author><host><volume>351</volume><pages><last>458</last><first>446</first></pages><issue>100</issue><author></author><title>Theoretical Computer Science Discrete Applied Mathematics</title><publicationDate>2000</publicationDate></host><title>Parameterized algorithms for feedback set problems and their duals in tournaments The complexity of irredundant sets parameterized by size</title><publicationDate>2000</publicationDate></json:item><json:item><author><json:item><name>F,V Fomin</name></json:item><json:item><name>F Grandoni</name></json:item><json:item><name>D Kratsch</name></json:item></author><host><volume>56</volume><issue>5</issue><author></author><title>Journal of the ACM</title><publicationDate>2009</publicationDate></host><title>A measure & conquer approach for the analysis of exact algorithms</title><publicationDate>2009</publicationDate></json:item><json:item><author><json:item><name>F,V Fomin</name></json:item><json:item><name>K Iwama</name></json:item><json:item><name>D Kratsch</name></json:item><json:item><name>P Kaski</name></json:item><json:item><name>M Koivisto</name></json:item><json:item><name>L Kowalik</name></json:item><json:item><name>Y Okamoto</name></json:item><json:item><name>J Van Rooij</name></json:item><json:item><name>R Williams</name></json:item></author><host><author></author><title>Moderately Exponential Time Algorithms. Dagstuhl Seminar Proceedings</title><publicationDate>2008</publicationDate></host><title>08431 Open problems – Moderately exponential time algorithms</title><publicationDate>2008</publicationDate></json:item><json:item><author><json:item><name>M Cygan</name></json:item><json:item><name>M Pilipczuk</name></json:item><json:item><name>J,O Wojtaszczyk</name></json:item></author><host><author></author><title>These proceedings</title></host><title>Irredundant set faster than O(2 n )</title></json:item><json:item><author><json:item><name>B Chor</name></json:item><json:item><name>M Fellows</name></json:item><json:item><name>D Juedes</name></json:item></author><host><volume>3353</volume><pages><last>269</last><first>257</first></pages><author></author><title>LNCS</title><publicationDate>2004</publicationDate></host><title>Linear kernels in linear time, or how to save k colors in O(n 2 ) steps</title><publicationDate>2004</publicationDate></json:item><json:item><author><json:item><name>M,R Fellows</name></json:item></author><host><pages><last>12</last><first>1</first></pages><author></author><title>WG 2003</title><publicationDate>2003</publicationDate></host><title>Blow-ups, win/win's, and crown rules: Some new directions in FPT</title><publicationDate>2003</publicationDate></json:item><json:item><author><json:item><name>J,A Telle</name></json:item></author><host><volume>1</volume><pages><last>171</last><first>157</first></pages><author></author><title>Nordic. J. of Comp</title><publicationDate>1994</publicationDate></host><title>Complexity of domination-type problems in graphs</title><publicationDate>1994</publicationDate></json:item><json:item><host><author><json:item><name>J,A Telle</name></json:item></author><title>Vertex Partitioning Problems: Characterization, Complexity and Algorithms on Partial k-Trees</title><publicationDate>1994</publicationDate></host></json:item></refBibs><genre><json:string>conference</json:string></genre><serie><editor><json:item><name>David Hutchison</name><affiliations><json:string>Lancaster University, Lancaster, UK</json:string></affiliations></json:item><json:item><name>Takeo Kanade</name><affiliations><json:string>Carnegie Mellon University, Pittsburgh, PA, USA</json:string></affiliations></json:item><json:item><name>Josef Kittler</name><affiliations><json:string>University of Surrey, Guildford, UK</json:string></affiliations></json:item><json:item><name>Jon M. 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>Tiziana Calamoneri</name><affiliations><json:string>Department of Computer Science, Sapienza University of Rome, Via Salaria 113, 00198, Rome, Italy</json:string><json:string>E-mail: calamo@di.uniroma1.it</json:string></affiliations></json:item><json:item><name>Josep Diaz</name><affiliations><json:string>Departament de Llenguatges i Sistemes Informatics, Universitat Politecnica de Catalunya, Campus Nord - Ed. Omega 240, Jordi Girona Salgado 1-3, 08034, Barcelona, Spain</json:string><json:string>E-mail: diaz@lsi.upc.edu</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>Data Structures</value></json:item><json:item><value>Numeric Computing</value></json:item><json:item><value>Computer Graphics</value></json:item><json:item><value>Computer Communication Networks</value></json:item></subject><isbn><json:string>978-3-642-13072-4</json:string></isbn><language><json:string>unknown</json:string></language><eissn><json:string>1611-3349</json:string></eissn><title>Algorithms and Complexity</title><bookId><json:string>978-3-642-13073-1</json:string></bookId><volume>6078</volume><pages><last>322</last><first>311</first></pages><issn><json:string>0302-9743</json:string></issn><genre><json:string>book-series</json:string></genre><eisbn><json:string>978-3-642-13073-1</json:string></eisbn><copyrightDate>2010</copyrightDate><doi><json:string>10.1007/978-3-642-13073-1</json:string></doi></host><publicationDate>2010</publicationDate><copyrightDate>2010</copyrightDate><doi><json:string>10.1007/978-3-642-13073-1_28</json:string></doi><id>D53E1C54122748DE8921D66B3B2ABDDBDB118DD2</id><score>0.27551985</score><fulltext><json:item><extension>pdf</extension><original>true</original><mimetype>application/pdf</mimetype><uri>https://api.istex.fr/document/D53E1C54122748DE8921D66B3B2ABDDBDB118DD2/fulltext/pdf</uri></json:item><json:item><extension>zip</extension><original>false</original><mimetype>application/zip</mimetype><uri>https://api.istex.fr/document/D53E1C54122748DE8921D66B3B2ABDDBDB118DD2/fulltext/zip</uri></json:item><istex:fulltextTEI uri="https://api.istex.fr/document/D53E1C54122748DE8921D66B3B2ABDDBDB118DD2/fulltext/tei"><teiHeader><fileDesc><titleStmt><title level="a" type="main" xml:lang="en">A Parameterized Route to Exact Puzzles: Breaking the 2 n -Barrier for Irredundance</title><title level="a" type="sub" xml:lang="en">(Extended Abstract)</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-Vralg Berlin Heidelberg, 2010</p></availability><date>2010</date></publicationStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a" type="main" xml:lang="en">A Parameterized Route to Exact Puzzles: Breaking the 2 n -Barrier for Irredundance</title><title level="a" type="sub" xml:lang="en">(Extended Abstract)</title><author xml:id="author-1"><persName><forename type="first">Daniel</forename><surname>Binkele-Raible</surname></persName><email>fernau@uni-trier.de</email><affiliation>FB 4—Abteilung Informatik, Universität Trier, D-54286, Trier, Germany</affiliation></author><author xml:id="author-2"><persName><forename type="first">Ljiljana</forename><surname>Brankovic</surname></persName><email>ljiljana.brankovic@newcastle.edu.au</email><affiliation>The University of Newcastle, University Drive, NSW 2308, Callaghan, Australia</affiliation></author><author xml:id="author-3"><persName><forename type="first">Henning</forename><surname>Fernau</surname></persName><email>raible@uni-trier.de</email><affiliation>FB 4—Abteilung Informatik, Universität Trier, D-54286, Trier, Germany</affiliation></author><author xml:id="author-4"><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-5"><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-6"><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-7"><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-8"><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">Algorithms and Complexity</title><title level="m" type="sub">7th International Conference, CIAC 2010, Rome, Italy, May 26-28, 2010. Proceedings</title><idno type="pISBN">978-3-642-13072-4</idno><idno type="eISBN">978-3-642-13073-1</idno><idno type="pISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="DOI">10.1007/978-3-642-13073-1</idno><idno type="book-ID">978-3-642-13073-1</idno><idno type="book-title-ID">211434</idno><idno type="book-sequence-number">6078</idno><idno type="book-volume-number">6078</idno><idno type="book-chapter-count">33</idno><editor><persName><forename type="first">Tiziana</forename><surname>Calamoneri</surname></persName><email>calamo@di.uniroma1.it</email><affiliation>Department of Computer Science, Sapienza University of Rome, Via Salaria 113, 00198, Rome, Italy</affiliation></editor><editor><persName><forename type="first">Josep</forename><surname>Diaz</surname></persName><email>diaz@lsi.upc.edu</email><affiliation>Departament de Llenguatges i Sistemes Informatics, Universitat Politecnica de Catalunya, Campus Nord - Ed. Omega 240, Jordi Girona Salgado 1-3, 08034, Barcelona, Spain</affiliation></editor><imprint><publisher>Springer Berlin Heidelberg</publisher><pubPlace>Berlin, Heidelberg</pubPlace><date type="published" when="2010"></date><biblScope unit="volume">6078</biblScope><biblScope unit="page" from="311">311</biblScope><biblScope unit="page" to="322">322</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">D53E1C54122748DE8921D66B3B2ABDDBDB118DD2</idno><idno type="DOI">10.1007/978-3-642-13073-1_28</idno><idno type="ChapterID">28</idno><idno type="ChapterID">Chap28</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>2010</date></creation><langUsage><language ident="en">en</language></langUsage><abstract xml:lang="en"><p>Abstract: The lower and the upper irredundance numbers of a graph G, denoted ir(G) and IR(G) respectively, are conceptually linked to domination and independence numbers and have numerous relations to other graph parameters. It is a long-standing open question whether determining these numbers for a graph G on n vertices admits exact algorithms running in time less than the trivial Ω(2 n ) enumeration barrier. We solve this open problem by devising parameterized algorithms for the duals of the natural parameterizations of the problems with running times faster than $\mathcal{O}^*(4^{k})$ . For example, we present an algorithm running in time $\mathcal{O}^*(3.069^{k}))$ for determining whether IR(G) is at least n − k. Although the corresponding problem has been shown to be in FPT by kernelization techniques, this paper offers the first parameterized algorithms with an exponential dependency on the parameter in the running time. Furthermore, these seem to be the first examples of a parameterized approach leading to a solution to a problem in exponential time algorithmics where the natural interpretation as exact exponential-time algorithms fails.</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>I15017</label><label>I1701X</label><label>I22013</label><label>I13022</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>Data Structures</term></item><item><term>Numeric Computing</term></item><item><term>Computer Graphics</term></item><item><term>Computer Communication Networks</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="2010">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/D53E1C54122748DE8921D66B3B2ABDDBDB118DD2/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 DisplayOrder="Western"><GivenName>Friedemann</GivenName><FamilyName>Mattern</FamilyName></EditorName></Editor><Editor AffiliationIDS="Aff6"><EditorName DisplayOrder="Western"><GivenName>John</GivenName><GivenName>C.</GivenName><FamilyName>Mitchell</FamilyName></EditorName></Editor><Editor AffiliationIDS="Aff7"><EditorName DisplayOrder="Western"><GivenName>Moni</GivenName><FamilyName>Naor</FamilyName></EditorName></Editor><Editor AffiliationIDS="Aff8"><EditorName DisplayOrder="Western"><GivenName>Oscar</GivenName><FamilyName>Nierstrasz</FamilyName></EditorName></Editor><Editor AffiliationIDS="Aff9"><EditorName DisplayOrder="Western"><GivenName>C.</GivenName><FamilyName>Pandu Rangan</FamilyName></EditorName></Editor><Editor AffiliationIDS="Aff10"><EditorName DisplayOrder="Western"><GivenName>Bernhard</GivenName><FamilyName>Steffen</FamilyName></EditorName></Editor><Editor AffiliationIDS="Aff11"><EditorName DisplayOrder="Western"><GivenName>Madhu</GivenName><FamilyName>Sudan</FamilyName></EditorName></Editor><Editor AffiliationIDS="Aff12"><EditorName DisplayOrder="Western"><GivenName>Demetri</GivenName><FamilyName>Terzopoulos</FamilyName></EditorName></Editor><Editor AffiliationIDS="Aff13"><EditorName DisplayOrder="Western"><GivenName>Doug</GivenName><FamilyName>Tygar</FamilyName></EditorName></Editor><Editor AffiliationIDS="Aff14"><EditorName DisplayOrder="Western"><GivenName>Moshe</GivenName><GivenName>Y.</GivenName><FamilyName>Vardi</FamilyName></EditorName></Editor><Editor AffiliationIDS="Aff15"><EditorName DisplayOrder="Western"><GivenName>Gerhard</GivenName><FamilyName>Weikum</FamilyName></EditorName></Editor><Affiliation ID="Aff1"><OrgName>Lancaster University</OrgName><OrgAddress><City>Lancaster</City><Country>UK</Country></OrgAddress></Affiliation><Affiliation ID="Aff2"><OrgName>Carnegie Mellon 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>978-3-642-13073-1</BookID><BookTitle>Algorithms and Complexity</BookTitle><BookSubTitle>7th International Conference, CIAC 2010, Rome, Italy, May 26-28, 2010. Proceedings</BookSubTitle><BookVolumeNumber>6078</BookVolumeNumber><BookSequenceNumber>6078</BookSequenceNumber><BookDOI>10.1007/978-3-642-13073-1</BookDOI><BookTitleID>211434</BookTitleID><BookPrintISBN>978-3-642-13072-4</BookPrintISBN><BookElectronicISBN>978-3-642-13073-1</BookElectronicISBN><BookChapterCount>33</BookChapterCount><BookCopyright><CopyrightHolderName>Springer-Vralg 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="I15017" Priority="3" Type="Secondary">Data Structures</BookSubject><BookSubject Code="I1701X" Priority="4" Type="Secondary">Numeric Computing</BookSubject><BookSubject Code="I22013" Priority="5" Type="Secondary">Computer Graphics</BookSubject><BookSubject Code="I13022" Priority="6" Type="Secondary">Computer Communication Networks</BookSubject><SubjectCollection Code="SUCO11645">Computer Science</SubjectCollection></BookSubjectGroup><BookContext><SeriesID>558</SeriesID></BookContext></BookInfo><BookHeader><EditorGroup><Editor AffiliationIDS="Aff16"><EditorName DisplayOrder="Western"><GivenName>Tiziana</GivenName><FamilyName>Calamoneri</FamilyName></EditorName><Contact><Email>calamo@di.uniroma1.it</Email></Contact></Editor><Editor AffiliationIDS="Aff17"><EditorName DisplayOrder="Western"><GivenName>Josep</GivenName><FamilyName>Diaz</FamilyName></EditorName><Contact><Email>diaz@lsi.upc.edu</Email></Contact></Editor><Affiliation ID="Aff16"><OrgDivision>Department of Computer Science</OrgDivision><OrgName>Sapienza University of Rome</OrgName><OrgAddress><Street>Via Salaria 113</Street><Postcode>00198</Postcode><City>Rome</City><Country>Italy</Country></OrgAddress></Affiliation><Affiliation ID="Aff17"><OrgDivision>Departament de Llenguatges i Sistemes Informatics</OrgDivision><OrgName>Universitat Politecnica de Catalunya</OrgName><OrgAddress><Street>Campus Nord - Ed. Omega 240, Jordi Girona Salgado 1-3</Street><Postcode>08034</Postcode><City>Barcelona</City><Country>Spain</Country></OrgAddress></Affiliation></EditorGroup></BookHeader><Part ID="Part8"><PartInfo TocLevels="0"><PartID>8</PartID><PartSequenceNumber>8</PartSequenceNumber><PartTitle>Session 7. Graph Algorithms II</PartTitle><PartChapterCount>5</PartChapterCount><PartContext><SeriesID>558</SeriesID><BookTitle>Algorithms and Complexity</BookTitle></PartContext></PartInfo><Chapter ID="Chap28" Language="En"><ChapterInfo ChapterType="OriginalPaper" ContainsESM="No" NumberingDepth="2" NumberingStyle="ContentOnly" TocLevels="0"><ChapterID>28</ChapterID><ChapterDOI>10.1007/978-3-642-13073-1_28</ChapterDOI><ChapterSequenceNumber>28</ChapterSequenceNumber><ChapterTitle Language="En">A Parameterized Route to Exact Puzzles: Breaking the 2<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>-Barrier for Irredundance</ChapterTitle><ChapterSubTitle Language="En">(Extended Abstract)</ChapterSubTitle><ChapterFirstPage>311</ChapterFirstPage><ChapterLastPage>322</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>8</PartID><BookID>978-3-642-13073-1</BookID><BookTitle>Algorithms and Complexity</BookTitle></ChapterContext></ChapterInfo><ChapterHeader><AuthorGroup><Author AffiliationIDS="Aff18"><AuthorName DisplayOrder="Western"><GivenName>Daniel</GivenName><FamilyName>Binkele-Raible</FamilyName></AuthorName><Contact><Email>fernau@uni-trier.de</Email></Contact></Author><Author AffiliationIDS="Aff19"><AuthorName DisplayOrder="Western"><GivenName>Ljiljana</GivenName><FamilyName>Brankovic</FamilyName></AuthorName><Contact><Email>ljiljana.brankovic@newcastle.edu.au</Email></Contact></Author><Author AffiliationIDS="Aff18"><AuthorName DisplayOrder="Western"><GivenName>Henning</GivenName><FamilyName>Fernau</FamilyName></AuthorName><Contact><Email>raible@uni-trier.de</Email></Contact></Author><Author AffiliationIDS="Aff20"><AuthorName DisplayOrder="Western"><GivenName>Joachim</GivenName><FamilyName>Kneis</FamilyName></AuthorName><Contact><Email>kneis@cs.rwth-aachen.de</Email></Contact></Author><Author AffiliationIDS="Aff21"><AuthorName DisplayOrder="Western"><GivenName>Dieter</GivenName><FamilyName>Kratsch</FamilyName></AuthorName><Contact><Email>kratsch@univ-metz.fr</Email></Contact></Author><Author AffiliationIDS="Aff20"><AuthorName DisplayOrder="Western"><GivenName>Alexander</GivenName><FamilyName>Langer</FamilyName></AuthorName><Contact><Email>langer@cs.rwth-aachen.de</Email></Contact></Author><Author AffiliationIDS="Aff22"><AuthorName DisplayOrder="Western"><GivenName>Mathieu</GivenName><FamilyName>Liedloff</FamilyName></AuthorName><Contact><Email>liedloff@univ-orleans.fr</Email></Contact></Author><Author AffiliationIDS="Aff20"><AuthorName DisplayOrder="Western"><GivenName>Peter</GivenName><FamilyName>Rossmanith</FamilyName></AuthorName><Contact><Email>rossmani@cs.rwth-aachen.de</Email></Contact></Author><Affiliation ID="Aff18"><OrgDivision>FB 4—Abteilung Informatik</OrgDivision><OrgName>Universität Trier</OrgName><OrgAddress><Postcode>D-54286</Postcode><City>Trier</City><Country>Germany</Country></OrgAddress></Affiliation><Affiliation ID="Aff19"><OrgName>The University of Newcastle</OrgName><OrgAddress><Street>University Drive</Street><Postcode>NSW 2308</Postcode><City>Callaghan</City><Country>Australia</Country></OrgAddress></Affiliation><Affiliation ID="Aff20"><OrgDivision>Department of Computer Science</OrgDivision><OrgName>RWTH Aachen University</OrgName><OrgAddress><Country>Germany</Country></OrgAddress></Affiliation><Affiliation ID="Aff21"><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="Aff22"><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>The lower and the upper irredundance numbers of a graph <Emphasis Type="Italic">G</Emphasis>, denoted ir(<Emphasis Type="Italic">G</Emphasis>) and IR(<Emphasis Type="Italic">G</Emphasis>) respectively, are conceptually linked to domination and independence numbers and have numerous relations to other graph parameters. It is a long-standing open question whether determining these numbers for a graph <Emphasis Type="Italic">G</Emphasis> on <Emphasis Type="Italic">n</Emphasis> vertices admits exact algorithms running in time less than the trivial Ω(2<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>) enumeration barrier. We solve this open problem by devising parameterized algorithms for the duals of the natural parameterizations of the problems with running times faster than <InlineEquation ID="IEq1"><InlineMediaObject><ImageObject FileRef="978-3-642-13073-1_28_Chapter_TeX2GIFIEq1.gif" Format="GIF" Color="BlackWhite" Type="Linedraw" Rendition="HTML"></ImageObject></InlineMediaObject><EquationSource Format="TEX">$\mathcal{O}^*(4^{k})$</EquationSource></InlineEquation>. For example, we present an algorithm running in time <InlineEquation ID="IEq2"><InlineMediaObject><ImageObject FileRef="978-3-642-13073-1_28_Chapter_TeX2GIFIEq2.gif" Format="GIF" Color="BlackWhite" Type="Linedraw" Rendition="HTML"></ImageObject></InlineMediaObject><EquationSource Format="TEX">$\mathcal{O}^*(3.069^{k}))$</EquationSource></InlineEquation> for determining whether IR(<Emphasis Type="Italic">G</Emphasis>) is at least <Emphasis Type="Italic">n</Emphasis> − <Emphasis Type="Italic">k</Emphasis>. Although the corresponding problem has been shown to be in FPT by kernelization techniques, this paper offers the first parameterized algorithms with an exponential dependency on the parameter in the running time. Furthermore, these seem to be the first examples of a parameterized approach leading to a solution to a problem in exponential time algorithmics where the natural interpretation as exact exponential-time algorithms fails.</Para></Abstract></ChapterHeader><NoBody></NoBody></Chapter></Part></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>A Parameterized Route to Exact Puzzles: Breaking the 2 n -Barrier for Irredundance</title><subTitle>(Extended Abstract)</subTitle></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>A Parameterized Route to Exact Puzzles: Breaking the 2 n -Barrier for Irredundance</title><subTitle>(Extended Abstract)</subTitle></titleInfo><name type="personal"><namePart type="given">Daniel</namePart><namePart type="family">Binkele-Raible</namePart><affiliation>FB 4—Abteilung Informatik, Universität Trier, 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">Ljiljana</namePart><namePart type="family">Brankovic</namePart><affiliation>The University of Newcastle, University Drive, NSW 2308, Callaghan, 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>FB 4—Abteilung Informatik, Universität Trier, 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">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">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">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: The lower and the upper irredundance numbers of a graph G, denoted ir(G) and IR(G) respectively, are conceptually linked to domination and independence numbers and have numerous relations to other graph parameters. It is a long-standing open question whether determining these numbers for a graph G on n vertices admits exact algorithms running in time less than the trivial Ω(2 n ) enumeration barrier. We solve this open problem by devising parameterized algorithms for the duals of the natural parameterizations of the problems with running times faster than $\mathcal{O}^*(4^{k})$ . For example, we present an algorithm running in time $\mathcal{O}^*(3.069^{k}))$ for determining whether IR(G) is at least n − k. Although the corresponding problem has been shown to be in FPT by kernelization techniques, this paper offers the first parameterized algorithms with an exponential dependency on the parameter in the running time. Furthermore, these seem to be the first examples of a parameterized approach leading to a solution to a problem in exponential time algorithmics where the natural interpretation as exact exponential-time algorithms fails.</abstract><relatedItem type="host"><titleInfo><title>Algorithms and Complexity</title><subTitle>7th International Conference, CIAC 2010, Rome, Italy, May 26-28, 2010. Proceedings</subTitle></titleInfo><name type="personal"><namePart type="given">Tiziana</namePart><namePart type="family">Calamoneri</namePart><affiliation>Department of Computer Science, Sapienza University of Rome, Via Salaria 113, 00198, Rome, Italy</affiliation><affiliation>E-mail: calamo@di.uniroma1.it</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Josep</namePart><namePart type="family">Diaz</namePart><affiliation>Departament de Llenguatges i Sistemes Informatics, Universitat Politecnica de Catalunya, Campus Nord - Ed. Omega 240, Jordi Girona Salgado 1-3, 08034, Barcelona, Spain</affiliation><affiliation>E-mail: diaz@lsi.upc.edu</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="I15017">Data Structures</topic><topic authority="SpringerSubjectCodes" authorityURI="I1701X">Numeric Computing</topic><topic authority="SpringerSubjectCodes" authorityURI="I22013">Computer Graphics</topic><topic authority="SpringerSubjectCodes" authorityURI="I13022">Computer Communication Networks</topic></subject><identifier type="DOI">10.1007/978-3-642-13073-1</identifier><identifier type="ISBN">978-3-642-13072-4</identifier><identifier type="eISBN">978-3-642-13073-1</identifier><identifier type="ISSN">0302-9743</identifier><identifier type="eISSN">1611-3349</identifier><identifier type="BookTitleID">211434</identifier><identifier type="BookID">978-3-642-13073-1</identifier><identifier type="BookChapterCount">33</identifier><identifier type="BookVolumeNumber">6078</identifier><identifier type="BookSequenceNumber">6078</identifier><identifier type="PartChapterCount">5</identifier><part><date>2010</date><detail type="part"><title>Session 7. Graph Algorithms II</title></detail><detail type="volume"><number>6078</number><caption>vol.</caption></detail><extent unit="pages"><start>311</start><end>322</end></extent></part><recordInfo><recordOrigin>Springer-Vralg Berlin Heidelberg, 2010</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">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-Vralg Berlin Heidelberg, 2010</recordOrigin></recordInfo></relatedItem><identifier type="istex">D53E1C54122748DE8921D66B3B2ABDDBDB118DD2</identifier><identifier type="DOI">10.1007/978-3-642-13073-1_28</identifier><identifier type="ChapterID">28</identifier><identifier type="ChapterID">Chap28</identifier><accessCondition type="use and reproduction" contentType="copyright">Springer-Vralg Berlin Heidelberg, 2010</accessCondition><recordInfo><recordContentSource>SPRINGER</recordContentSource><recordOrigin>Springer-Verlag Berlin Heidelberg, 2010</recordOrigin></recordInfo></mods></metadata></istex></record>Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Rhénanie/explor/UnivTrevesV1/Data/Istex/Corpus
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 001B33 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Istex/Corpus/biblio.hfd -nk 001B33 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien
|wiki= Wicri/Rhénanie
|area= UnivTrevesV1
|flux= Istex
|étape= Corpus
|type= RBID
|clé= ISTEX:D53E1C54122748DE8921D66B3B2ABDDBDB118DD2
|texte= A Parameterized Route to Exact Puzzles: Breaking the 2 n -Barrier for Irredundance
}}
| This area was generated with Dilib version V0.6.31. |  |