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      • Theses - Department of Computer Engineering
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      Decomposing linear programs for parallel solution

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      Author
      Pınar, Ali
      Advisor
      Aykanat, Cevdet
      Date
      1996
      Publisher
      Bilkent University
      Language
      English
      Type
      Thesis
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      Abstract
      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 Matrices
      Block Angular Form
      Hypergraph Partitioning
      Graph Partitioning by Node Separator
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      http://hdl.handle.net/11693/17802
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      • Dept. of Computer Engineering - Master's degree 511
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