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An Effective Model to Decompose Linear Programs for Parallel Solution ?

Summary: An Effective Model to Decompose Linear
Programs for Parallel Solution ?
Ali Pinar and Cevdet Aykanat
Computer Engineering Department
Bilkent University, Ankara, Turkey
Abstract. Although inherent parallelism in the solution of block an­
gular Linear Programming (LP) problems has been exploited in many
research works, the literature that addresses decomposing constraint ma­
trices into block angular form for parallel solution is very rare and re­
cent. We have previously proposed hypergraph models, which reduced
the problem to the hypergraph partitioning problem. However, the qual­
ity 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 well­known 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.


Source: Aykanat, Cevdet - Department of Computer Engineering, Bilkent University


Collections: Computer Technologies and Information Sciences