Lower bounds for the majority communication complexity of various graph accessibility problems
Identifieur interne : 000E59 ( Istex/Corpus ); précédent : 000E58; suivant : 000E60Lower bounds for the majority communication complexity of various graph accessibility problems
Auteurs : C. Meinel ; S. WaackSource :
- Mathematical systems theory [ 0025-5661 ] ; 1996-12-01.
Abstract
Abstract: We investigate the probabilistic communication complexity (more exactly, the majority communication complexity), of the graph accessibility problem (GAP) and its counting versions MOD k -GAP,k ≥ 2. Due to arguments concerning matrix variation ranks and certain projection reductions, we prove that, for any partition of the input variables, GAP and MOD m -GAP have majority communication complexity Ω,(n), wheren denotes the number of nodes of the graph under consideration.
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DOI: 10.1007/BF01301969
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<OrgAddress><Postcode>D-54286</Postcode>
<City>Trier</City>
<Country>Germany</Country>
</OrgAddress>
</Affiliation>
<Affiliation ID="Aff2"><OrgDivision>Institut für Numerisch und Angewandte Mathematik</OrgDivision>
<OrgName>Universität Göttingen</OrgName>
<OrgAddress><Street>Lotzestrasse 16–18</Street>
<Postcode>D-37083</Postcode>
<City>Gottingen</City>
<Country>Germany</Country>
</OrgAddress>
</Affiliation>
</AuthorGroup>
<Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading>
<Para>We investigate the probabilistic communication complexity (more exactly, the majority communication complexity), of the graph accessibility problem (GAP) and its counting versions MOD<Subscript><Emphasis Type="Italic">k</Emphasis>
</Subscript>
-GAP,<Emphasis Type="Italic">k</Emphasis>
≥ 2. Due to arguments concerning matrix variation ranks and certain projection reductions, we prove that, for any partition of the input variables, GAP and MOD<Subscript><Emphasis Type="Italic">m</Emphasis>
</Subscript>
-GAP have majority communication complexity Ω,(<Emphasis Type="Italic">n</Emphasis>
), where<Emphasis Type="Italic">n</Emphasis>
denotes the number of nodes of the graph under consideration.</Para>
</Abstract>
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<mods version="3.6"><titleInfo lang="en"><title>Lower bounds for the majority communication complexity of various graph accessibility problems</title>
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<titleInfo type="alternative" contentType="CDATA" lang="en"><title>Lower bounds for the majority communication complexity of various graph accessibility problems</title>
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<name type="personal"><namePart type="given">C.</namePart>
<namePart type="family">Meinel</namePart>
<affiliation>Theoretische Informatik, Fachbereich IV, Universität Trier, D-54286, Trier, Germany</affiliation>
<role><roleTerm type="text">author</roleTerm>
</role>
</name>
<name type="personal"><namePart type="given">S.</namePart>
<namePart type="family">Waack</namePart>
<affiliation>Institut für Numerisch und Angewandte Mathematik, Universität Göttingen, Lotzestrasse 16–18, D-37083, Gottingen, Germany</affiliation>
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<originInfo><publisher>Springer-Verlag</publisher>
<place><placeTerm type="text">New York</placeTerm>
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<dateCreated encoding="w3cdtf">1994-05-15</dateCreated>
<dateIssued encoding="w3cdtf">1996-12-01</dateIssued>
<copyrightDate encoding="w3cdtf">1996</copyrightDate>
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<abstract lang="en">Abstract: We investigate the probabilistic communication complexity (more exactly, the majority communication complexity), of the graph accessibility problem (GAP) and its counting versions MOD k -GAP,k ≥ 2. Due to arguments concerning matrix variation ranks and certain projection reductions, we prove that, for any partition of the input variables, GAP and MOD m -GAP have majority communication complexity Ω,(n), wheren denotes the number of nodes of the graph under consideration.</abstract>
<relatedItem type="host"><titleInfo><title>Mathematical systems theory</title>
</titleInfo>
<titleInfo type="abbreviated"><title>Math. Systems Theory</title>
</titleInfo>
<genre type="journal" displayLabel="Archive Journal"></genre>
<originInfo><dateIssued encoding="w3cdtf">1996-12-01</dateIssued>
<copyrightDate encoding="w3cdtf">1996</copyrightDate>
</originInfo>
<subject><genre>Journal-Subject-Group</genre>
<topic authority="SpringerSubjectCodes" authorityURI="I">Computer Science</topic>
<topic authority="SpringerSubjectCodes" authorityURI="I16005">Theory of Computation</topic>
<topic authority="SpringerSubjectCodes" authorityURI="M1400X">Computational Mathematics and Numerical Analysis</topic>
</subject>
<identifier type="ISSN">0025-5661</identifier>
<identifier type="eISSN">1433-0490</identifier>
<identifier type="JournalID">224</identifier>
<identifier type="IssueArticleCount">7</identifier>
<identifier type="VolumeIssueCount">6</identifier>
<part><date>1996</date>
<detail type="volume"><number>29</number>
<caption>vol.</caption>
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<detail type="issue"><number>6</number>
<caption>no.</caption>
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<extent unit="pages"><start>649</start>
<end>659</end>
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<identifier type="istex">124CE07576FB24F78DE893936DB7F0FBCD68C918</identifier>
<identifier type="DOI">10.1007/BF01301969</identifier>
<identifier type="ArticleID">BF01301969</identifier>
<identifier type="ArticleID">Art6</identifier>
<accessCondition type="use and reproduction" contentType="copyright">Springer-Verlag New York Inc, 1996</accessCondition>
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