Messages Scheduling for Data Redistribution between Clusters
Identifieur interne : 002E75 ( Istex/Corpus ); précédent : 002E74; suivant : 002E76Messages Scheduling for Data Redistribution between Clusters
Auteurs : Johanne Cohen ; Emmanuel Jeannot ; Nicolas PadoySource :
- Lecture Notes in Computer Science [ 0302-9743 ]
Abstract
Abstract: In this paper we study the general problem of parallel data redistribution over a network. Given a set of communications between two parallel machines interconnected by a backbone, we wish to minimize the total time required for the completion of all communications assuming that communications can be preempted and that preemption comes with an extra cost. Our problem, called k-Preemptive bipartite scheduling (KPBS) is proven to be NP-Complete. Moreover we prove that approximating KPBS problem within a ratio number smaller that $\frac{4}{3}$ is impossible unless P=NP. In spite of this negative result, we study a lower bound on the cost of KPBS problem in terms of its parameters, and we propose an approximation algorithm with ratio 2 and fast heuristics.
Url:
DOI: 10.1007/978-3-540-24669-5_116
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ISTEX:C4FA7996F58BD4FBBFF37EEACFAE0111E3AFDB7ALe document en format XML
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Moreover we prove that approximating KPBS problem within a ratio number smaller that $\frac{4}{3}$ is impossible unless P=NP. 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Given a set of communications between two parallel machines interconnected by a backbone, we wish to minimize the total time required for the completion of all communications assuming that communications can be preempted and that preemption comes with an extra cost. Our problem, called <hi rend="italic">k-Preemptive bipartite scheduling (KPBS)</hi> is proven to be NP-Complete. Moreover we prove that approximating KPBS problem within a ratio number smaller that <formula xml:id="IEq1" notation="TEX"><media mimeType="image" url=""></media>$\frac{4}{3}$
</formula> is impossible unless <hi rend="italic">P</hi>=NP. In spite of this negative result, we study a lower bound on the cost of KPBS problem in terms of its parameters, and we propose an approximation algorithm with ratio 2 and fast heuristics.</p></abstract><textClass ana="subject"><keywords scheme="book-subject-collection"><list><label>SUCO11645</label><item><term>Computer Science</term></item></list></keywords></textClass><textClass ana="subject"><keywords scheme="book-subject"><list><label>I</label><item><term type="Primary">Computer Science</term></item><label>I14002</label><item><term type="Secondary" subtype="priority-1">Software Engineering/Programming and Operating Systems</term></item><label>I16021</label><item><term type="Secondary" subtype="priority-2">Algorithm Analysis and Problem Complexity</term></item><label>I17001</label><item><term type="Secondary" subtype="priority-3">Mathematics of Computing</term></item><label>I12034</label><item><term type="Secondary" subtype="priority-4">Memory 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University</OrgName><OrgAddress><City>CA</City><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff6"><OrgName>University of Bern</OrgName><OrgAddress><Country>Switzerland</Country></OrgAddress></Affiliation><Affiliation ID="Aff7"><OrgName>Indian Institute of Technology</OrgName><OrgAddress><City>Madras</City><Country>India</Country></OrgAddress></Affiliation><Affiliation ID="Aff8"><OrgName>Dortmund University</OrgName><OrgAddress><Country>Germany</Country></OrgAddress></Affiliation><Affiliation ID="Aff9"><OrgName>New York University</OrgName><OrgAddress><City>NY</City><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff10"><OrgName>University of California at Berkeley</OrgName><OrgAddress><City>CA</City><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff11"><OrgName>Rice University</OrgName><OrgAddress><City>Houston</City><State>TX</State><Country>USA</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>978-3-540-24669-5</BookID><BookTitle>Parallel Processing and Applied Mathematics</BookTitle><BookSubTitle>5th International Conference, PPAM 2003, Czestochowa, Poland, September 7-10, 2003. Revised Papers</BookSubTitle><BookVolumeNumber>3019</BookVolumeNumber><BookSequenceNumber>3019</BookSequenceNumber><BookDOI>10.1007/b97218</BookDOI><BookTitleID>82439</BookTitleID><BookPrintISBN>978-3-540-21946-0</BookPrintISBN><BookElectronicISBN>978-3-540-24669-5</BookElectronicISBN><BookChapterCount>149</BookChapterCount><BookCopyright><CopyrightHolderName>Springer-Verlag Berlin Heidelberg</CopyrightHolderName><CopyrightYear>2004</CopyrightYear></BookCopyright><BookSubjectGroup><BookSubject Code="I" Type="Primary">Computer Science</BookSubject><BookSubject Code="I14002" Priority="1" Type="Secondary">Software Engineering/Programming and Operating Systems</BookSubject><BookSubject Code="I16021" Priority="2" Type="Secondary">Algorithm Analysis and Problem Complexity</BookSubject><BookSubject Code="I17001" Priority="3" Type="Secondary">Mathematics of Computing</BookSubject><BookSubject Code="I12034" Priority="4" Type="Secondary">Memory Structures</BookSubject><BookSubject Code="I13022" Priority="5" Type="Secondary">Computer Communication Networks</BookSubject><BookSubject Code="M1400X" Priority="6" Type="Secondary">Computational Mathematics and Numerical Analysis</BookSubject><SubjectCollection Code="SUCO11645">Computer Science</SubjectCollection></BookSubjectGroup><BookContext><SeriesID>558</SeriesID></BookContext></BookInfo><BookHeader><EditorGroup><Editor AffiliationIDS="Aff12"><EditorName DisplayOrder="Western"><GivenName>Roman</GivenName><FamilyName>Wyrzykowski</FamilyName></EditorName><Contact><Email>roman@icis.pcz.pl</Email></Contact></Editor><Editor AffiliationIDS="Aff13"><EditorName DisplayOrder="Western"><GivenName>Jack</GivenName><FamilyName>Dongarra</FamilyName></EditorName><Contact><Email>dongarra@eecs.utk.edu</Email></Contact></Editor><Editor AffiliationIDS="Aff14"><EditorName DisplayOrder="Western"><GivenName>Marcin</GivenName><FamilyName>Paprzycki</FamilyName></EditorName><Contact><Email>marcin.paprzycki@ibspan.waw.pl</Email></Contact></Editor><Editor AffiliationIDS="Aff15"><EditorName DisplayOrder="Western"><GivenName>Jerzy</GivenName><FamilyName>Waśniewski</FamilyName></EditorName><Contact><Email>jw@imm.dtu.dk</Email></Contact></Editor><Affiliation ID="Aff12"><OrgDivision>Institute of Computational and Information Sciences</OrgDivision><OrgName>Czestochowa University of Technology</OrgName><OrgAddress><Country> </Country></OrgAddress></Affiliation><Affiliation ID="Aff13"><OrgDivision>Computer Science Department</OrgDivision><OrgName>University of Tennessee</OrgName><OrgAddress><Postcode>TN 37996-3450</Postcode><City>Knoxville</City><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff14"><OrgDivision>Systems Research Institute</OrgDivision><OrgName>Polish Academy of Science</OrgName><OrgAddress><City>Warsaw</City><Country>Poland</Country></OrgAddress></Affiliation><Affiliation ID="Aff15"><OrgDivision>Informatics & Mathematical Modeling</OrgDivision><OrgName>Technical University of Denmark</OrgName><OrgAddress><Postcode>DK-2800</Postcode><City>Lyngby</City><Country>Denmark</Country></OrgAddress></Affiliation></EditorGroup></BookHeader><Part ID="Part14"><PartInfo TocLevels="0"><PartID>14</PartID><PartSequenceNumber>14</PartSequenceNumber><PartTitle>HeteroPar’03</PartTitle><PartChapterCount>10</PartChapterCount><PartContext><SeriesID>558</SeriesID><BookTitle>Parallel Processing and Applied Mathematics</BookTitle></PartContext></PartInfo><Chapter ID="Chap116" Language="En"><ChapterInfo ChapterType="OriginalPaper" ContainsESM="No" NumberingDepth="2" NumberingStyle="ContentOnly" TocLevels="0"><ChapterID>116</ChapterID><ChapterDOI>10.1007/978-3-540-24669-5_116</ChapterDOI><ChapterSequenceNumber>116</ChapterSequenceNumber><ChapterTitle Language="En">Messages Scheduling for Data Redistribution between Clusters</ChapterTitle><ChapterFirstPage>896</ChapterFirstPage><ChapterLastPage>906</ChapterLastPage><ChapterCopyright><CopyrightHolderName>Springer-Verlag Berlin Heidelberg</CopyrightHolderName><CopyrightYear>2004</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>14</PartID><BookID>978-3-540-24669-5</BookID><BookTitle>Parallel Processing and Applied Mathematics</BookTitle></ChapterContext></ChapterInfo><ChapterHeader><AuthorGroup><Author AffiliationIDS="Aff16"><AuthorName DisplayOrder="Western"><GivenName>Johanne</GivenName><FamilyName>Cohen</FamilyName></AuthorName><Contact><Email>jcohen@loria.fr</Email></Contact></Author><Author AffiliationIDS="Aff17"><AuthorName DisplayOrder="Western"><GivenName>Emmanuel</GivenName><FamilyName>Jeannot</FamilyName></AuthorName><Contact><Email>ejeannot@loria.fr</Email></Contact></Author><Author AffiliationIDS="Aff18"><AuthorName DisplayOrder="Western"><GivenName>Nicolas</GivenName><FamilyName>Padoy</FamilyName></AuthorName><Contact><Email>npadoy@ens-lyon.fr</Email></Contact></Author><Affiliation ID="Aff16"><OrgName>CNRS LORIA</OrgName><OrgAddress><City>Vandœuvre les Nancy</City><Country>France</Country></OrgAddress></Affiliation><Affiliation ID="Aff17"><OrgDivision>LORIA</OrgDivision><OrgName>Université H. Poincaré</OrgName><OrgAddress><City>Vandœuvre les Nancy</City><Country>France</Country></OrgAddress></Affiliation><Affiliation ID="Aff18"><OrgName>École Normale Supérieure de Lyon</OrgName><OrgAddress><Country>France</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>In this paper we study the general problem of parallel data redistribution over a network. Given a set of communications between two parallel machines interconnected by a backbone, we wish to minimize the total time required for the completion of all communications assuming that communications can be preempted and that preemption comes with an extra cost. Our problem, called <Emphasis Type="Italic">k-Preemptive bipartite scheduling (KPBS)</Emphasis> is proven to be NP-Complete. Moreover we prove that approximating KPBS problem within a ratio number smaller that <InlineEquation ID="IEq1"><InlineMediaObject><ImageObject FileRef="978-3-540-24669-5_116_Chapter_TeX2GIFIEq1.gif" Format="GIF" Color="BlackWhite" Type="Linedraw" Rendition="HTML"></ImageObject></InlineMediaObject><EquationSource Format="TEX">$\frac{4}{3}$</EquationSource></InlineEquation> is impossible unless <Emphasis Type="Italic">P</Emphasis>=NP. In spite of this negative result, we study a lower bound on the cost of KPBS problem in terms of its parameters, and we propose an approximation algorithm with ratio 2 and fast heuristics.</Para></Abstract><ArticleNote Type="Misc"><SimplePara>This work is partially supported by the ARC INRIA redGRID</SimplePara></ArticleNote></ChapterHeader><NoBody></NoBody></Chapter></Part></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Messages Scheduling for Data Redistribution between Clusters</title></titleInfo><titleInfo type="alternative" contentType="CDATA"><title>Messages Scheduling for Data Redistribution between Clusters</title></titleInfo><name type="personal"><namePart type="given">Johanne</namePart><namePart type="family">Cohen</namePart><affiliation>CNRS LORIA, Vandœuvre les Nancy, France</affiliation><affiliation>E-mail: jcohen@loria.fr</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Emmanuel</namePart><namePart type="family">Jeannot</namePart><affiliation>LORIA, Université H. Poincaré, Vandœuvre les Nancy, France</affiliation><affiliation>E-mail: ejeannot@loria.fr</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Nicolas</namePart><namePart type="family">Padoy</namePart><affiliation>École Normale Supérieure de Lyon, France</affiliation><affiliation>E-mail: npadoy@ens-lyon.fr</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre displayLabel="OriginalPaper" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" type="conference" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-BFHXPBJJ-3">conference</genre><originInfo><publisher>Springer Berlin Heidelberg</publisher><place><placeTerm type="text">Berlin, Heidelberg</placeTerm></place><dateIssued encoding="w3cdtf">2004</dateIssued><copyrightDate encoding="w3cdtf">2004</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><abstract lang="en">Abstract: In this paper we study the general problem of parallel data redistribution over a network. Given a set of communications between two parallel machines interconnected by a backbone, we wish to minimize the total time required for the completion of all communications assuming that communications can be preempted and that preemption comes with an extra cost. Our problem, called k-Preemptive bipartite scheduling (KPBS) is proven to be NP-Complete. Moreover we prove that approximating KPBS problem within a ratio number smaller that $\frac{4}{3}$ is impossible unless P=NP. In spite of this negative result, we study a lower bound on the cost of KPBS problem in terms of its parameters, and we propose an approximation algorithm with ratio 2 and fast heuristics.</abstract><relatedItem type="host"><titleInfo><title>Parallel Processing and Applied Mathematics</title><subTitle>5th International Conference, PPAM 2003, Czestochowa, Poland, September 7-10, 2003. Revised Papers</subTitle></titleInfo><name type="personal"><namePart type="given">Roman</namePart><namePart type="family">Wyrzykowski</namePart><affiliation>Institute of Computational and Information Sciences, Czestochowa University of Technology, </affiliation><affiliation>E-mail: roman@icis.pcz.pl</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Jack</namePart><namePart type="family">Dongarra</namePart><affiliation>Computer Science Department, University of Tennessee, TN 37996-3450, Knoxville, USA</affiliation><affiliation>E-mail: dongarra@eecs.utk.edu</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Marcin</namePart><namePart type="family">Paprzycki</namePart><affiliation>Systems Research Institute, Polish Academy of Science, Warsaw, Poland</affiliation><affiliation>E-mail: marcin.paprzycki@ibspan.waw.pl</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Jerzy</namePart><namePart type="family">Waśniewski</namePart><affiliation>Informatics & Mathematical Modeling, Technical University of Denmark, DK-2800, Lyngby, Denmark</affiliation><affiliation>E-mail: jw@imm.dtu.dk</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><genre type="book-series" authority="ISTEX" authorityURI="https://publication-type.data.istex.fr" valueURI="https://publication-type.data.istex.fr/ark:/67375/JMC-0G6R5W5T-Z">book-series</genre><originInfo><publisher>Springer</publisher><copyrightDate encoding="w3cdtf">2004</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="I14002">Software Engineering/Programming and Operating Systems</topic><topic authority="SpringerSubjectCodes" authorityURI="I16021">Algorithm Analysis and Problem Complexity</topic><topic authority="SpringerSubjectCodes" authorityURI="I17001">Mathematics of Computing</topic><topic authority="SpringerSubjectCodes" authorityURI="I12034">Memory Structures</topic><topic authority="SpringerSubjectCodes" authorityURI="I13022">Computer Communication Networks</topic><topic authority="SpringerSubjectCodes" authorityURI="M1400X">Computational Mathematics and Numerical Analysis</topic></subject><identifier type="DOI">10.1007/b97218</identifier><identifier type="ISBN">978-3-540-21946-0</identifier><identifier type="eISBN">978-3-540-24669-5</identifier><identifier type="ISSN">0302-9743</identifier><identifier type="eISSN">1611-3349</identifier><identifier type="BookTitleID">82439</identifier><identifier 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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, 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, CA, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Oscar</namePart><namePart 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