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Coarse-grained parallel transitive closure algorithm: Path decomposition technique

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dc.contributor.author Gibbons, A en
dc.contributor.author Pagourtzis, A en
dc.contributor.author Potapov, I en
dc.contributor.author Rytter, W en
dc.date.accessioned 2014-03-01T01:18:46Z
dc.date.available 2014-03-01T01:18:46Z
dc.date.issued 2003 en
dc.identifier.issn 0010-4620 en
dc.identifier.uri https://dspace.lib.ntua.gr/xmlui/handle/123456789/15185
dc.subject Coarse Grained en
dc.subject Transitive Closure en
dc.subject.classification Computer Science, Hardware & Architecture en
dc.subject.classification Computer Science, Information Systems en
dc.subject.classification Computer Science, Software Engineering en
dc.subject.other Computation theory en
dc.subject.other Dynamic programming en
dc.subject.other Mathematical transformations en
dc.subject.other Matrix algebra en
dc.subject.other Generic transitive closure problems en
dc.subject.other Parallel algorithms en
dc.title Coarse-grained parallel transitive closure algorithm: Path decomposition technique en
heal.type journalArticle en
heal.identifier.primary 10.1093/comjnl/46.4.391 en
heal.identifier.secondary http://dx.doi.org/10.1093/comjnl/46.4.391 en
heal.language English en
heal.publicationDate 2003 en
heal.abstract We investigate the relation between fine-grained and coarse-grained distributed computations of a class of problems related to the generic transitive closure problem (TC for short). We choose an intricate systolic algorithm for the TC problem, by Guibas, Kung and Thompson (GKT algorithm for short), as a starting point due to its particularly close relationship to matrix multiplication. The GKT algorithm reduces the TC problem to three successive parallel matrix multiplications. We extract the main ideas of this algorithm, namely different path decompositions related to min-paths and max-paths computations and devise a two-pass parallel algorithm, such that the second pass is purely a triangular matrix multiplication involving exactly 1/3 of the total number of elementary operations (multiplying two single elements of the matrix). This is helpful in coarse-grained parallel computations since matrix multiplication is well parallelizable. A novel approach is used and as a first result a more efficient and simpler two-pass fine-grained algorithm is designed. The second result is a non-trivial transformation of this fine-grained algorithm into a coarse-grained (and more practical) version. The full proof of correctness of the transformation, which is presented in the appendices, is quite complex and is the hardest result of the paper. Our algorithms are specially structured to directly show the correspondence between the main fine-grained and the main coarse-grained operations. en
heal.publisher OXFORD UNIV PRESS en
heal.journalName Computer Journal en
dc.identifier.doi 10.1093/comjnl/46.4.391 en
dc.identifier.isi ISI:000183528100004 en
dc.identifier.volume 46 en
dc.identifier.issue 4 en
dc.identifier.spage 391 en
dc.identifier.epage 400 en


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