cient Massively Parallel Implementation of Some Combinatorial Algorithms 1

We describe our implementation of several e cient parallel algorithms on the massively parallel SIMD machine MasPar MP-1 with virtual processing. The MPL language that we used on the MasPar MP-1 does not support virtual processing. In this paper, we describe the implementation of virtual processing for several combinatorial algorithms using the MPL language. We present our data allocation scheme for virtual processing and code rewriting rules for converting a code that uses no virtual processors into a code with virtual processing. We then describe the implementation of virtual processing and the ne-tuning of a set of commonly used routines. In coding these routines, we tried di erent underlying (deterministic and randomized) algorithms. We present the performance data for our di erent implementations. We also compared the performance of several of the parallel routines with their sequential implementations. The performance of our code tracks theoretical predictions quite well for the range of values for virtual processing that we tested. We used techniques presented in this paper to convert non-virtual processing code for undirected graph algorithms into virtual processing code. Our experimental data suggests that by using our techniques, one can implement parallel algorithms with virtual processing quite e ectively on the MasPar MP-1 using the MPL language. Preprint, accepted for publication in Theoretical Computer Science 1996