Decomposing linear programs for parallel solution
Author
Pınar, Ali
Advisor
Aykanat, Cevdet
Date
1996Publisher
Bilkent University
Language
English
Type
ThesisItem Usage Stats
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Show full item recordAbstract
Many current research efforts are based on better exploitation of sparsity—
common in most large scaled problems—for computational efEciency. This work
proposes different methods for permuting sparse matrices to block angular form
with specified number of equal sized blocks for efficient parallelism. The problem
has applications in linear programming, where there is a lot of work on the solution
of problems with existing block angular structure. However, these works
depend on the existing block angular structure of the matrix, and hence suffer
from unscalability. We propose two hypergraph models for decomposition,
and these models reduce the problem to the well-known hypergraph partitioning
problem. We also propose a graph model, which reduces the problem to the
graph partitioning by node separator problem. We were able to decompose very
large problems, the results are quite attractive both in terms solution quality and
running times.
Keywords
Sparse MatricesBlock Angular Form
Hypergraph Partitioning
Graph Partitioning by Node Separator