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Decomposing Linear Programs for Parallel Solution?

Summary: Decomposing Linear Programs for
Parallel Solution?
Ali P nar, Umit V. Catalyurek, Cevdet Aykanat Mustafa P nar??
Computer Engineering Department Industrial Engineering Department
Bilkent University, Ankara, Turkey Bilkent University, Ankara, Turkey
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 su er
from unscalability and load imbalance since they exploit only the exist-
ing block angular structure of the LP constraint matrix. In this paper,
we consider decomposing LP constraint matrices to obtain block angular
structures with speci ed number of blocks for scalable parallelization. We
propose hypergraph models to represent LP constraint matrices for de-
composition. 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 experi-
menting 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.


Source: Aykanat, Cevdet - Department of Computer Engineering, Bilkent University
Çatalyürek, Ümit V. - Departments of Biomedical Informatics & Electrical and Computer Engineering, Ohio State University


Collections: Computer Technologies and Information Sciences