Minimum communication cost reordering for parallel sparse Cholesky factorization

In this paper, we consider the problem of reducing the communication cost for the parallel factorization of a sparse symmetric positive definite matrix on a distributed-memory multiprocessor. We define a parallel communication cost function and show that, with a contrived example, simply minimizing...

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Vydáno v:Parallel computing Ročník 25; číslo 8; s. 943 - 967
Hlavní autoři: Lin, Wen-Yang, Chen, Chuen-Liang
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 1999
Témata:
Communication cost
Distributed-memory multiprocessor
Elimination tree
Equivalent reordering
Parallel factorization
Sparse matrix
Sparse matrix
Parallel factorization
Elimination tree
Equivalent reordering
Distributed-memory multiprocessor
Communication cost
ISSN:0167-8191, 1872-7336
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Shrnutí:In this paper, we consider the problem of reducing the communication cost for the parallel factorization of a sparse symmetric positive definite matrix on a distributed-memory multiprocessor. We define a parallel communication cost function and show that, with a contrived example, simply minimizing the height of the elimination tree is ineffective for exploiting minimum communication cost and the discrepancy may grow infinitely. We propose an algorithm to find an ordering such that the communication cost to complete the parallel Cholesky factorization is minimum among all equivalent reorderings. Our algorithm consumes O( nlog n+ m) in time, where n is the number of nodes and m the sum of all maximal clique sizes in the filled graph.
Bibliografie:ObjectType-Article-2
SourceType-Scholarly Journals-1
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ISSN:0167-8191
1872-7336
DOI:10.1016/S0167-8191(99)00027-7