On the PVM Computations of Transitive Closure and Algebraic Path Problems

We investigate experimentally, alternative approaches to the distributed parallel computation of a class of problems related to the generic transitive closure problem and the algebraic path problem. Our main result is the comparison of two parallel algorithms for transitive closure, { a straightforward coarse-grained parallel implementation of the Warshall algorithm named Block-Processing (which also extends to the stronger algebraic path problem) and { a coarse-grained Three-Pass algorithm, introduced in this paper. Although this latter algorithm is more complicated, it behaves better for large problem sizes. We show the relationship between the transitive closure problem and matrix mulipli-cation ; the latter problem has especially eecient PVM implementations which can be applied here. The synchronous shared memory model and several known intricate systolic algorithms are a good starting point for distributed implementations. We discuss alternative implementations and the suitability of the PVM model.