A parallel interior point algorithm for linear programming on a network of transputers

Interior Point algorithms have become a very successful tool for solving large-scale linear programming problems. The Dual Affine algorithm is one of the Interior Point algorithms implemented in the computer program OB1. It is a good candidate for implementation on a parallel computer because it is very computing-intensive. A parallel Dual Affine algorithm is presented which is suitable for a parallel computer with a distributed memory. The algorithm obtains its speedup from parallel sparse linear algebra computations such as Cholesky factorisation, matrix multiplication, and triangular system solving, which form the bulk of the computing work. Efficient algorithms based on the grid distribution of matrices are presented for each of these computations. The algorithm is implemented in occam 2 on a square mesh of transputers. The resulting parallel program is connected to the sequentialFortran 77 program OB1, which performs the preprocessing and the postprocessing. Experimental results on a mesh of 400 transputers are given for a test set of seven realistic planning and scheduling problems from Shell and seven problems from the NETLIB LP collection; the results show a speedup of 88 for the largest problem.