Abstract
Parallelizing sparse Simplex algorithms is one of the most challenging problems in computational science. We implemented the revised Simplex algorithm with LU decomposition on the Touchstone Delta and the iPSC/2. Because of very sparse matrices and very heavy communication, the ratio of computation to communication is extremely low. It becomes necessary to carefully select parallel algorithms, partitioning patterns, and communication optimization to achieve a reasonable speedup. Satisfactory performance has been obtained for a class of LP problems with high n/ m ratios.
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