Lower bounds for the modular communication complexity of various graph accessibility problems
Identifieur interne : 000C30 ( Istex/Corpus ); précédent : 000C29; suivant : 000C31Lower bounds for the modular communication complexity of various graph accessibility problems
Auteurs : Christoph Meinel ; Stephan WaackSource :
- Lecture Notes in Computer Science [ 0302-9743 ] ; 1995.
Abstract
Abstract: We investigate the modular communication complexity of the graph accessibility problem GAP and its modular counting versions MODk-GAP, k≥2. Due to arguments concerning variation ranks and certain projection reductions, we prove that, for any partition of the input variables and for any moduls k and m, GAP and MODk-GAP have MOD m -communication complexity Ω(n), where n denotes the number of nodes of the graphs under consideration.
Url:
DOI: 10.1007/3-540-59175-3_107
Links to Exploration step
ISTEX:D9B2BCFCF8E1CAA608E9808C8CBEE49C06CFFEB8Le document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">Lower bounds for the modular communication complexity of various graph accessibility problems</title><author><name sortKey="Meinel, Christoph" sort="Meinel, Christoph" uniqKey="Meinel C" first="Christoph" last="Meinel">Christoph Meinel</name><affiliation><mods:affiliation>Theoretische Informatik Fachbereich IV, Universität Trier, D-54286, Trier</mods:affiliation></affiliation></author><author><name sortKey="Waack, Stephan" sort="Waack, Stephan" uniqKey="Waack S" first="Stephan" last="Waack">Stephan Waack</name><affiliation><mods:affiliation>Inst. für Num. und Angew. Mathematik, Georg-August-Univ. Göttingen, Lotzestr. 16–18, D-37083, Göttingen</mods:affiliation></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:D9B2BCFCF8E1CAA608E9808C8CBEE49C06CFFEB8</idno><date when="1995" year="1995">1995</date><idno type="doi">10.1007/3-540-59175-3_107</idno><idno type="url">https://api.istex.fr/document/D9B2BCFCF8E1CAA608E9808C8CBEE49C06CFFEB8/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">000C30</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">000C30</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Lower bounds for the modular communication complexity of various graph accessibility problems</title><author><name sortKey="Meinel, Christoph" sort="Meinel, Christoph" uniqKey="Meinel C" first="Christoph" last="Meinel">Christoph Meinel</name><affiliation><mods:affiliation>Theoretische Informatik Fachbereich IV, Universität Trier, D-54286, Trier</mods:affiliation></affiliation></author><author><name sortKey="Waack, Stephan" sort="Waack, Stephan" uniqKey="Waack S" first="Stephan" last="Waack">Stephan Waack</name><affiliation><mods:affiliation>Inst. für Num. und Angew. Mathematik, Georg-August-Univ. Göttingen, Lotzestr. 16–18, D-37083, Göttingen</mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="s">Lecture Notes in Computer Science</title><imprint><date>1995</date></imprint><idno type="ISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="ISSN">0302-9743</idno></series><idno type="istex">D9B2BCFCF8E1CAA608E9808C8CBEE49C06CFFEB8</idno><idno type="DOI">10.1007/3-540-59175-3_107</idno><idno type="ChapterID">31</idno><idno type="ChapterID">Chap31</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: We investigate the modular communication complexity of the graph accessibility problem GAP and its modular counting versions MODk-GAP, k≥2. Due to arguments concerning variation ranks and certain projection reductions, we prove that, for any partition of the input variables and for any moduls k and m, GAP and MODk-GAP have MOD m -communication complexity Ω(n), where n denotes the number of nodes of the graphs under consideration.</div></front></TEI><istex><corpusName>springer</corpusName><author><json:item><name>Christoph Meinel</name><affiliations><json:string>Theoretische Informatik Fachbereich IV, Universität Trier, D-54286, Trier</json:string></affiliations></json:item><json:item><name>Stephan Waack</name><affiliations><json:string>Inst. für Num. und Angew. Mathematik, Georg-August-Univ. Göttingen, Lotzestr. 16–18, D-37083, Göttingen</json:string></affiliations></json:item></author><language><json:string>eng</json:string></language><originalGenre><json:string>ReviewPaper</json:string></originalGenre><abstract>Abstract: We investigate the modular communication complexity of the graph accessibility problem GAP and its modular counting versions MODk-GAP, k≥2. Due to arguments concerning variation ranks and certain projection reductions, we prove that, for any partition of the input variables and for any moduls k and m, GAP and MODk-GAP have MOD m -communication complexity Ω(n), where n denotes the number of nodes of the graphs under consideration.</abstract><qualityIndicators><score>4.94</score><pdfVersion>1.3</pdfVersion><pdfPageSize>439.208 x 666 pts</pdfPageSize><refBibsNative>false</refBibsNative><keywordCount>0</keywordCount><abstractCharCount>443</abstractCharCount><pdfWordCount>4124</pdfWordCount><pdfCharCount>16252</pdfCharCount><pdfPageCount>9</pdfPageCount><abstractWordCount>68</abstractWordCount></qualityIndicators><title>Lower bounds for the modular communication complexity of various graph accessibility problems</title><chapterId><json:string>31</json:string><json:string>Chap31</json:string></chapterId><refBibs><json:item><host><pages><last>183</last><first>133</first></pages><author><json:item><name>A,V Aho</name></json:item><json:item><name>J,D Ullman</name></json:item><json:item><name>M Yannakakis</name></json:item></author><title>On notions of information transfer ill VLSI circuits, in: Proe. 15th ACM STOC</title><publicationDate>1983</publicationDate></host></json:item><json:item><author><json:item><name>L Babai</name></json:item><json:item><name>P Frankl</name></json:item><json:item><name>J Simon</name></json:item></author><host><pages><last>347</last><first>337</first></pages><author></author><title>Proc. 27th IEEE FOCS</title><publicationDate>1986</publicationDate></host><title>Gbmplexity classes in communication complexity theoly</title><publicationDate>1986</publicationDate></json:item><json:item><author><json:item><name>B Halstenberg</name></json:item><json:item><name>R Reischuk</name></json:item></author><host><pages><last>28</last><first>19</first></pages><author></author><title>Proe. 3rd IEEE Structure in Complexity Theory Conference</title><publicationDate>1988</publicationDate></host><publicationDate>1988</publicationDate></json:item><json:item><author><json:item><name>C Datum</name></json:item><json:item><name>M Krause</name></json:item><json:item><name> Ch</name></json:item><json:item><name> Meinel</name></json:item><json:item><name> St</name></json:item><json:item><name> Waack</name></json:item></author><host><pages><last>293</last><first>281</first></pages><author></author><title>Proc. 9th STACS</title><publicationDate>1992</publicationDate></host><title>Separating counting communication complexity classes</title><publicationDate>1992</publicationDate></json:item><json:item><author><json:item><name>A Hajnal</name></json:item><json:item><name>W Maass</name></json:item><json:item><name>G Turan</name></json:item></author><host><pages><last>191</last><first>186</first></pages><author></author><title>Proc. 20th ACM STOC</title><publicationDate>1988</publicationDate></host><title>On the communication complexity of graph problems</title><publicationDate>1988</publicationDate></json:item><json:item><author><json:item><name>N Immerman</name></json:item></author><host><pages><last>778</last><first>760</first></pages><author></author><title>Languages that capture complexity classes</title><publicationDate>1978</publicationDate></host><publicationDate>1978</publicationDate></json:item><json:item><author><json:item><name>M Krause</name></json:item><json:item><name> St</name></json:item><json:item><name> Waack</name></json:item></author><host><pages><last>782</last><first>777</first></pages><author></author><title>Proc. 32nd IEEE FOCS</title><publicationDate>1991</publicationDate></host><title>Variation ranks of communication matrices and lower bounds for depth two circuits having symmetric gates with unbounded fan-in</title><publicationDate>1991</publicationDate></json:item><json:item><author><json:item><name> Ch</name></json:item></author><host><pages><last>535</last><first>527</first></pages><author></author><title>Projection reducibility and the complexity c/asses L(nonunifol3n) and NLOmnuniforn O Proc. 12th MFCS</title><publicationDate>1986</publicationDate></host><publicationDate>1986</publicationDate></json:item><json:item><author><json:item><name> Ch</name></json:item></author><host><author></author><title>Modified branching programs and their computational power</title><publicationDate>1989</publicationDate></host><publicationDate>1989</publicationDate></json:item><json:item><author><json:item><name>Ch Meinel</name></json:item><json:item><name> St</name></json:item><json:item><name> Waack</name></json:item></author><host><pages><last>290</last><first>273</first></pages><author></author><title>Eds. K. Amhos-Spies</title><publicationDate>1993</publicationDate></host><title>Upper and lower bounds for certain graph-accessibility problems on bounded alternating w-branching prog~'ams, in: Complexity Theory current research</title><publicationDate>1993</publicationDate></json:item><json:item><author><json:item><name>W Savitch</name></json:item></author><host><volume>4</volume><pages><last>253</last><first>244</first></pages><author></author><title>J. Comput. System Sci</title><publicationDate>1970</publicationDate></host><title>Relationship between nondeterministic and deterministic tape complexities</title><publicationDate>1970</publicationDate></json:item><json:item><host><pages><last>253</last><first>244</first></pages><author><json:item><name>L,V Skyum</name></json:item><json:item><name> Valiant</name></json:item></author><title>A complexity theoxy based on Boolean algebra, Proe</title></host></json:item><json:item><author><json:item><name>A Yao</name></json:item></author><host><pages><last>311</last><first>308</first></pages><author></author><title>Proc. 13th ACM STOC</title><publicationDate>1981</publicationDate></host><title>The entropic limitations of VLSI computations</title><publicationDate>1981</publicationDate></json:item><json:item><host><pages><last>627</last><first>619</first></pages><author><json:item><name>A Yao</name></json:item></author><title>On ACC and Threshold Circuits, Proe</title></host></json:item></refBibs><genre><json:string>conference</json:string></genre><serie><editor><json:item><name>Gerhard Goos</name></json:item><json:item><name>Juris Hartmanis</name></json:item><json:item><name>Jan van Leeuwen</name></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>1995</copyrightDate></serie><host><editor><json:item><name>Ricardo Baeza-Yates</name></json:item><json:item><name>Eric Goles</name></json:item><json:item><name>Patricio V. Poblete</name></json:item></editor><subject><json:item><value>Computer Science</value></json:item><json:item><value>Computer Science</value></json:item><json:item><value>Computation by Abstract Devices</value></json:item><json:item><value>Algorithm Analysis and Problem Complexity</value></json:item><json:item><value>Logics and Meanings of Programs</value></json:item><json:item><value>Combinatorics</value></json:item></subject><isbn><json:string>978-3-540-59175-7</json:string></isbn><language><json:string>unknown</json:string></language><eissn><json:string>1611-3349</json:string></eissn><title>LATIN '95: Theoretical Informatics</title><bookId><json:string>3540591753</json:string></bookId><volume>911</volume><pages><last>435</last><first>427</first></pages><issn><json:string>0302-9743</json:string></issn><genre><json:string>book-series</json:string></genre><eisbn><json:string>978-3-540-49220-7</json:string></eisbn><copyrightDate>1995</copyrightDate><doi><json:string>10.1007/3-540-59175-3</json:string></doi></host><publicationDate>2005</publicationDate><copyrightDate>1995</copyrightDate><doi><json:string>10.1007/3-540-59175-3_107</json:string></doi><id>D9B2BCFCF8E1CAA608E9808C8CBEE49C06CFFEB8</id><score>0.46913168</score><fulltext><json:item><extension>pdf</extension><original>true</original><mimetype>application/pdf</mimetype><uri>https://api.istex.fr/document/D9B2BCFCF8E1CAA608E9808C8CBEE49C06CFFEB8/fulltext/pdf</uri></json:item><json:item><extension>zip</extension><original>false</original><mimetype>application/zip</mimetype><uri>https://api.istex.fr/document/D9B2BCFCF8E1CAA608E9808C8CBEE49C06CFFEB8/fulltext/zip</uri></json:item><istex:fulltextTEI uri="https://api.istex.fr/document/D9B2BCFCF8E1CAA608E9808C8CBEE49C06CFFEB8/fulltext/tei"><teiHeader><fileDesc><titleStmt><title level="a" type="main" xml:lang="en">Lower bounds for the modular communication complexity of various graph accessibility problems</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, 1995</p></availability><date>1995</date></publicationStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a" type="main" xml:lang="en">Lower bounds for the modular communication complexity of various graph accessibility problems</title><author xml:id="author-1"><persName><forename type="first">Christoph</forename><surname>Meinel</surname></persName><affiliation>Theoretische Informatik Fachbereich IV, Universität Trier, D-54286, Trier</affiliation></author><author xml:id="author-2"><persName><forename type="first">Stephan</forename><surname>Waack</surname></persName><affiliation>Inst. für Num. und Angew. Mathematik, Georg-August-Univ. Göttingen, Lotzestr. 16–18, D-37083, Göttingen</affiliation></author></analytic><monogr><title level="m">LATIN '95: Theoretical Informatics</title><title level="m" type="sub">Second Latin American Symposium Valparaíso, Chile, April 3–7, 1995 Proceedings</title><idno type="pISBN">978-3-540-59175-7</idno><idno type="eISBN">978-3-540-49220-7</idno><idno type="pISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="DOI">10.1007/3-540-59175-3</idno><idno type="book-ID">3540591753</idno><idno type="book-title-ID">42662</idno><idno type="book-volume-number">911</idno><idno type="book-chapter-count">38</idno><editor><persName><forename type="first">Ricardo</forename><surname>Baeza-Yates</surname></persName></editor><editor><persName><forename type="first">Eric</forename><surname>Goles</surname></persName></editor><editor><persName><forename type="first">Patricio</forename><forename type="first">V.</forename><surname>Poblete</surname></persName></editor><imprint><publisher>Springer Berlin Heidelberg</publisher><pubPlace>Berlin, Heidelberg</pubPlace><date type="published" when="2005-06-06"></date><biblScope unit="volume">911</biblScope><biblScope unit="page" from="427">427</biblScope><biblScope unit="page" to="435">435</biblScope></imprint></monogr><series><title level="s">Lecture Notes in Computer Science</title><editor><persName><forename type="first">Gerhard</forename><surname>Goos</surname></persName></editor><editor><persName><forename type="first">Juris</forename><surname>Hartmanis</surname></persName></editor><editor><persName><forename type="first">Jan</forename><surname>van Leeuwen</surname></persName></editor><biblScope><date>1995</date></biblScope><idno type="pISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="series-Id">558</idno></series><idno type="istex">D9B2BCFCF8E1CAA608E9808C8CBEE49C06CFFEB8</idno><idno type="DOI">10.1007/3-540-59175-3_107</idno><idno type="ChapterID">31</idno><idno type="ChapterID">Chap31</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>1995</date></creation><langUsage><language ident="en">en</language></langUsage><abstract xml:lang="en"><p>Abstract: We investigate the modular communication complexity of the graph accessibility problem GAP and its modular counting versions MODk-GAP, k≥2. Due to arguments concerning variation ranks and certain projection reductions, we prove that, for any partition of the input variables and for any moduls k and m, GAP and MODk-GAP have MOD m -communication complexity Ω(n), where n denotes the number of nodes of the graphs under consideration.</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>I16013</label><label>I16021</label><label>I1603X</label><label>M17009</label><item><term>Computer Science</term></item><item><term>Computation by Abstract Devices</term></item><item><term>Algorithm Analysis and Problem Complexity</term></item><item><term>Logics and Meanings of Programs</term></item><item><term>Combinatorics</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="2005-06-06">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/D9B2BCFCF8E1CAA608E9808C8CBEE49C06CFFEB8/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 TocLevels="0"><SeriesID>558</SeriesID><SeriesPrintISSN>0302-9743</SeriesPrintISSN><SeriesElectronicISSN>1611-3349</SeriesElectronicISSN><SeriesTitle Language="En">Lecture Notes in Computer Science</SeriesTitle><SeriesAbbreviatedTitle>Lect Notes Comput Sci</SeriesAbbreviatedTitle></SeriesInfo><SeriesHeader><EditorGroup><Editor><EditorName DisplayOrder="Western"><GivenName>Gerhard</GivenName><FamilyName>Goos</FamilyName></EditorName></Editor><Editor><EditorName DisplayOrder="Western"><GivenName>Juris</GivenName><FamilyName>Hartmanis</FamilyName></EditorName></Editor><Editor><EditorName DisplayOrder="Western"><GivenName>Jan</GivenName><Particle>van</Particle><FamilyName>Leeuwen</FamilyName></EditorName></Editor></EditorGroup></SeriesHeader><Book Language="En"><BookInfo MediaType="eBook" Language="En" BookProductType="Proceedings" TocLevels="0" NumberingStyle="Unnumbered"><BookID>3540591753</BookID><BookTitle>LATIN '95: Theoretical Informatics</BookTitle><BookSubTitle>Second Latin American Symposium Valparaíso, Chile, April 3–7, 1995 Proceedings</BookSubTitle><BookVolumeNumber>911</BookVolumeNumber><BookDOI>10.1007/3-540-59175-3</BookDOI><BookTitleID>42662</BookTitleID><BookPrintISBN>978-3-540-59175-7</BookPrintISBN><BookElectronicISBN>978-3-540-49220-7</BookElectronicISBN><BookChapterCount>38</BookChapterCount><BookCopyright><CopyrightHolderName>Springer-Verlag</CopyrightHolderName><CopyrightYear>1995</CopyrightYear></BookCopyright><BookSubjectGroup><BookSubject Code="I" Type="Primary">Computer Science</BookSubject><BookSubject Code="I16013" Priority="1" Type="Secondary">Computation by Abstract Devices</BookSubject><BookSubject Code="I16021" Priority="2" Type="Secondary">Algorithm Analysis and Problem Complexity</BookSubject><BookSubject Code="I1603X" Priority="3" Type="Secondary">Logics and Meanings of Programs</BookSubject><BookSubject Code="M17009" Priority="4" Type="Secondary">Combinatorics</BookSubject><SubjectCollection Code="SUCO11645">Computer Science</SubjectCollection></BookSubjectGroup></BookInfo><BookHeader><EditorGroup><Editor><EditorName DisplayOrder="Western"><GivenName>Ricardo</GivenName><FamilyName>Baeza-Yates</FamilyName></EditorName></Editor><Editor><EditorName DisplayOrder="Western"><GivenName>Eric</GivenName><FamilyName>Goles</FamilyName></EditorName></Editor><Editor><EditorName DisplayOrder="Western"><GivenName>Patricio</GivenName><GivenName>V.</GivenName><FamilyName>Poblete</FamilyName></EditorName></Editor></EditorGroup></BookHeader><Chapter ID="Chap31" Language="En"><ChapterInfo ChapterType="ReviewPaper" NumberingStyle="Unnumbered" TocLevels="0" ContainsESM="No"><ChapterID>31</ChapterID><ChapterDOI>10.1007/3-540-59175-3_107</ChapterDOI><ChapterSequenceNumber>31</ChapterSequenceNumber><ChapterTitle Language="En">Lower bounds for the modular communication complexity of various graph accessibility problems</ChapterTitle><ChapterFirstPage>427</ChapterFirstPage><ChapterLastPage>435</ChapterLastPage><ChapterCopyright><CopyrightHolderName>Springer-Verlag</CopyrightHolderName><CopyrightYear>1995</CopyrightYear></ChapterCopyright><ChapterHistory><OnlineDate><Year>2005</Year><Month>6</Month><Day>6</Day></OnlineDate></ChapterHistory><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>3540591753</BookID><BookTitle>LATIN '95: Theoretical Informatics</BookTitle></ChapterContext></ChapterInfo><ChapterHeader><AuthorGroup><Author AffiliationIDS="Aff1"><AuthorName DisplayOrder="Western"><GivenName>Christoph</GivenName><FamilyName>Meinel</FamilyName></AuthorName></Author><Author AffiliationIDS="Aff2"><AuthorName DisplayOrder="Western"><GivenName>Stephan</GivenName><FamilyName>Waack</FamilyName></AuthorName></Author><Affiliation ID="Aff1"><OrgDivision>Theoretische Informatik Fachbereich IV</OrgDivision><OrgName>Universität Trier</OrgName><OrgAddress><Postcode>D-54286</Postcode><City>Trier</City></OrgAddress></Affiliation><Affiliation ID="Aff2"><OrgDivision>Inst. für Num. und Angew. Mathematik</OrgDivision><OrgName>Georg-August-Univ. Göttingen</OrgName><OrgAddress><Street>Lotzestr. 16–18</Street><Postcode>D-37083</Postcode><City>Göttingen</City></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>We investigate the modular communication complexity of the graph accessibility problem GAP and its modular counting versions MOD<Subscript>k</Subscript>-GAP, <Emphasis Type="Italic">k</Emphasis>≥2. Due to arguments concerning variation ranks and certain projection reductions, we prove that, for any partition of the input variables and for any moduls <Emphasis Type="Italic">k</Emphasis> and <Emphasis Type="Italic">m</Emphasis>, GAP and MOD<Subscript>k</Subscript>-GAP have <Emphasis Type="Italic">MOD</Emphasis><Subscript><Emphasis Type="Italic">m</Emphasis></Subscript>-communication complexity <Emphasis Type="Italic">Ω(n)</Emphasis>, where <Emphasis Type="Italic">n</Emphasis> denotes the number of nodes of the graphs under consideration.</Para></Abstract><KeywordGroup Language="En"><Heading>Topics</Heading><Keyword>Computational Complexity</Keyword><Keyword>Modular Communication Protocols</Keyword><Keyword>Variation ranks</Keyword><Keyword>Projection Reductions</Keyword><Keyword>GAP, MOD<Subscript>k</Subscript>-GAP</Keyword></KeywordGroup></ChapterHeader><NoBody></NoBody></Chapter></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Lower bounds for the modular communication complexity of various graph accessibility problems</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Lower bounds for the modular communication complexity of various graph accessibility problems</title></titleInfo><name type="personal"><namePart type="given">Christoph</namePart><namePart type="family">Meinel</namePart><affiliation>Theoretische Informatik Fachbereich IV, Universität Trier, D-54286, Trier</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Stephan</namePart><namePart type="family">Waack</namePart><affiliation>Inst. für Num. und Angew. Mathematik, Georg-August-Univ. Göttingen, Lotzestr. 16–18, D-37083, Göttingen</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="conference" displayLabel="ReviewPaper"></genre><originInfo><publisher>Springer Berlin Heidelberg</publisher><place><placeTerm type="text">Berlin, Heidelberg</placeTerm></place><dateIssued encoding="w3cdtf">2005-06-06</dateIssued><copyrightDate encoding="w3cdtf">1995</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType></physicalDescription><abstract lang="en">Abstract: We investigate the modular communication complexity of the graph accessibility problem GAP and its modular counting versions MODk-GAP, k≥2. Due to arguments concerning variation ranks and certain projection reductions, we prove that, for any partition of the input variables and for any moduls k and m, GAP and MODk-GAP have MOD m -communication complexity Ω(n), where n denotes the number of nodes of the graphs under consideration.</abstract><relatedItem type="host"><titleInfo><title>LATIN '95: Theoretical Informatics</title><subTitle>Second Latin American Symposium Valparaíso, Chile, April 3–7, 1995 Proceedings</subTitle></titleInfo><name type="personal"><namePart type="given">Ricardo</namePart><namePart type="family">Baeza-Yates</namePart><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Eric</namePart><namePart type="family">Goles</namePart><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Patricio</namePart><namePart type="given">V.</namePart><namePart type="family">Poblete</namePart><role><roleTerm type="text">editor</roleTerm></role></name><genre type="book-series" displayLabel="Proceedings"></genre><originInfo><copyrightDate encoding="w3cdtf">1995</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="I16013">Computation by Abstract Devices</topic><topic authority="SpringerSubjectCodes" authorityURI="I16021">Algorithm Analysis and Problem Complexity</topic><topic authority="SpringerSubjectCodes" authorityURI="I1603X">Logics and Meanings of Programs</topic><topic authority="SpringerSubjectCodes" authorityURI="M17009">Combinatorics</topic></subject><identifier type="DOI">10.1007/3-540-59175-3</identifier><identifier type="ISBN">978-3-540-59175-7</identifier><identifier type="eISBN">978-3-540-49220-7</identifier><identifier type="ISSN">0302-9743</identifier><identifier type="eISSN">1611-3349</identifier><identifier type="BookTitleID">42662</identifier><identifier type="BookID">3540591753</identifier><identifier type="BookChapterCount">38</identifier><identifier type="BookVolumeNumber">911</identifier><part><date>1995</date><detail type="volume"><number>911</number><caption>vol.</caption></detail><extent unit="pages"><start>427</start><end>435</end></extent></part><recordInfo><recordOrigin>Springer-Verlag, 1995</recordOrigin></recordInfo></relatedItem><relatedItem type="series"><titleInfo><title>Lecture Notes in Computer Science</title></titleInfo><name type="personal"><namePart type="given">Gerhard</namePart><namePart type="family">Goos</namePart><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Juris</namePart><namePart type="family">Hartmanis</namePart><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Jan</namePart><namePart type="family">van Leeuwen</namePart><role><roleTerm type="text">editor</roleTerm></role></name><originInfo><copyrightDate encoding="w3cdtf">1995</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, 1995</recordOrigin></recordInfo></relatedItem><identifier type="istex">D9B2BCFCF8E1CAA608E9808C8CBEE49C06CFFEB8</identifier><identifier type="DOI">10.1007/3-540-59175-3_107</identifier><identifier type="ChapterID">31</identifier><identifier type="ChapterID">Chap31</identifier><accessCondition type="use and reproduction" contentType="copyright">Springer-Verlag, 1995</accessCondition><recordInfo><recordContentSource>SPRINGER</recordContentSource><recordOrigin>Springer-Verlag, 1995</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 000C30 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Istex/Corpus/biblio.hfd -nk 000C30 | 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:D9B2BCFCF8E1CAA608E9808C8CBEE49C06CFFEB8
|texte= Lower bounds for the modular communication complexity of various graph accessibility problems
}}
| This area was generated with Dilib version V0.6.31. |  |