Decomposing linear programs for parallel solution

Date
1995-08
Advisor
Instructor
Source Title
Second International Workshop on Applied Parallel Computing Computations in Physics, Chemistry and Engineering Science, PARA '95
Print ISSN
0302-9743
Electronic ISSN
Publisher
Springer
Volume
Issue
Pages
473 - 482
Language
English
Type
Conference Paper
Journal Title
Journal ISSN
Volume Title
Abstract

Coarse grain parallelism inherent in the solution of Linear Programming (LP) problems with block angular constraint matrices has been exploited in recent research works. However, these approaches suffer from unscalability and load imbalance since they exploit only the existing block angular structure of the LP constraint matrix. In this paper, we consider decomposing LP constraint matrices to obtain block angular structures with specified number of blocks for scalable parallelization. We propose hypergraph models to represent LP constraint matrices for decomposition. In these models, the decomposition problem reduces to the well-known hypergraph partitioning problem. A Kernighan-Lin based multiway hypergraph partitioning heuristic is implemented for experimenting with the performance of the proposed hypergraph models on the decomposition of the LP problems selected from NETLIB suite. Initial results are promising and justify further research on other hypergraph partitioning heuristics for decomposing large LP problems. © Springer-Verlag Berlin Heidelberg 1996.

Course
Other identifiers
Book Title
Keywords
Linear programming, Angular constraint, Block-angular structure, Decomposition problems, Hypergraph partitioning, Number of blocks, Parallel solutions, Parallelizations, Recent researches, Matrix algebra
Citation
Published Version (Please cite this version)