Efficient parallel implementation of transitive closure of digraphs

Abstract

Based on a CGM/BSP parallel algorithm for computing the transitive closure of an acyclic directed graph (digraph), we present a modified version that works for any digraph and show very promising implementation results. The original CGM/BSP algorithm for acyclic digraphs uses a linear extension labeling of the vertices. With this labeling, the original algorithm can be shown to require log p + 1 communication rounds, where p is the number of processors. The modified CGM/BSP algorithm works for any digraph and does not use the linear extension labeling. In theory the modified version no longer guarantees the O(log p) bound on the number of communication rounds, as shown by an artificially elaborated example that requires more than log p + 1 communication rounds. In practice, however, all the graphs tested use at most log p + 1 communication rounds. The implementation results are very promising and show the efficiency and scalability of the proposed modified algorithm, and compare favorably with other parallel implementations. © Springer-Verlag Berlin Heidelberg 2003.