Sparse Implementation of Revised Simplex Algorithmson

Parallelizing sparse simplex algorithms is one of the most challenging problems. 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 speedup. Two implementations on Intel hypercubes are presented in this paper. The experimental results show that a nearly linear speedup can be obtained with the basic revised simplex algorithm. However, the basic revised simplex algorithm has many ll-ins. We also implement a revised simplex algorithm with LU decomposition. It is a very sparse algorithm, and it is very diicult to achieve a speedup with it.