Encapsulating multiple communication-cost metrics in partitioning sparse rectangular matrices for parallel matrix-vector multiplies

Date

2004

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Abstract

This paper addresses the problem of one-dimensional partitioning of structurally unsymmetric square and rectangular sparse matrices for parallel matrix-vector and matrix-transpose-vector multiplies. The objective is to minimize the communication cost while maintaining the balance on computational loads of processors. Most of the existing partitioning models consider only the total message volume hoping that minimizing this communication-cost metric is likely to reduce other metrics. However, the total message latency (start-up time) may be more important than the total message volume. Furthermore, the maximum message volume and latency handled by a single processor are also important metrics. We propose a two-phase approach that encapsulates all these four communication-cost metrics. The objective in the first phase is to minimize the total message volume while maintaining the computational-load balance. The objective in the second phase is to encapsulate the remaining three communication-cost metrics. We propose communication-hypergraph and partitioning models for the second phase. We then present several methods for partitioning communication hypergraphs. Experiments on a wide range of test matrices show that the proposed approach yields very effective partitioning results. A parallel implementation on a PC cluster verifies that the theoretical improvements shown by partitioning results hold in practice.

Source Title

SIAM Journal on Scientific Computing

Publisher

SIAM

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Keywords

Communication hypergraph, Hypergraph partitioning, Iterative method, Matrix partitioning, Matrix-vector multiply, Message latency, Message volume, Parallel computing, Rectangular matrix, Structurally unsymmetric matrix, Communication hypergraph, Hypergraph partitioning, Matrix partitioning, Matrix-vector multiply, Message latency, Message volume, Rectangular matrix, Structurally unsymmetric matrix, Computational methods, Costs, Graph theory, Iterative methods, Metric system, Parallel processing systems, Vectors, Matrix algebra

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Published Version (Please cite this version)

Language

English

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Article