A Parallelization of Dijkstra's Shortest Path Algorithm

The single source shortest path (SSSP) problem lacks parallel solutions which are fast and simultaneously work-eecient. We propose simple criteria which divide Dijkstra's sequential SSSP algorithm into a number of phases, such that the operations within a phase can be done in parallel. We give a PRAM algorithm based on these criteria and analyze its performance on random digraphs with random edge weights uniformly distributed in 0; 1]. We use the G(n; d=n) model: the graph consists of n nodes and each edge is chosen with probability d=n. Our PRAM algorithm needs O(n 1=3 log n) time and O(n log n+dn) work with high probability (whp). We also give extensions to external memory computation. Simulations show the applicability of our approach even on non-random graphs.