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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Bibliographic Details
Published in:Parallel computing Vol. 25; no. 8; pp. 943 - 967
Main Authors: Lin, Wen-Yang, Chen, Chuen-Liang
Format: Journal Article
Language:English
Published: Elsevier B.V 1999
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0167-8191
1872-7336
DOI:10.1016/S0167-8191(99)00027-7