Coarse-grained parallel transitive closure algorithm: Path decomposition technique

Gibbons, A; Pagourtzis, A; Potapov, I; Rytter, W

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