Parallel network dual simplex method on a shared memory multiprocessor

We present a parallel algorithm for solving the dual transshipment problem. The traditional dual simplex method does not offer much scope for parallelization, because it moves from one basic feasible solution to another, performing one pivot operation at a time. We present a new method called modified network dual simplex method which uses concurrent pivots. This departure from the traditional LP approach raises several issues such as the need to convert a non-basic feasible solution to a basic feasible solution. We present our strategies to handle these issues as well as the corresponding parallel algorithms. We also present results of testing this algorithm on large graphs to solve the integrated layout compaction and wire balancing problem