An effective model to decompose linear programs for parallel solution

Date
1996-08
Advisor
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Source Title
Applied Parallel Computing Industrial Computation and Optimization Third International Workshop, PARA '96
Print ISSN
0302-9743
Electronic ISSN
Publisher
Springer
Volume
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Pages
592 - 601
Language
English
Type
Conference Paper
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Abstract

Although inherent parallelism in the solution of block angulax Linear Programming (LP) problems has been exploited in many research works, the literature that addresses decomposing constraint matrices into block angular form for parallel solution is very rare and recent. We have previously proposed hypergraph models, which reduced the problem to the hypergraph partitioning problem. However, the quality of the results reported were limited due to the hypergraph partitioning tools we have used. Very recently, multilevel graph partitioning heuristics have been proposed leading to very successful graph partitioning tools; Chaco and Metis. In this paper, we propose an effective graph model to decompose matrices into block angular form, which reduces the problem to the well-known graph partitioning by vertex separator problem. We have experimented the validity of our proposed model with various LP problems selected from NETLIB and other sources. The results are very attractive both in terms of solution quality and running times. © Springer-Verlag Berlin Heidelberg 1996.

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Keywords
Linear programming, Matrix algebra, Optimization, Graph partitioning, Graph partitioning by vertex separators, Hypergraph model, Hypergraph partitioning, Inherent parallelism, Multilevel graph partitioning, Parallel solutions, Solution quality, Graph theory
Citation
Published Version (Please cite this version)