Scalable Single Source Shortest Path Algorithms for Massively Parallel Systems

We consider the single-source shortest path (SSSP) problem: given an undirected graph with integer edge weights and a source vertex $v$ , find the shortest paths from $v$ to all other vertices. In this paper, we introduce a novel parallel algorithm, derived from the Bellman-Ford and Delta-stepping algorithms. We employ various pruning techniques, such as edge classification and direction-optimization, to dramatically reduce inter-node communication traffic, and we propose load balancing strategies to handle higher-degree vertices. These techniques are particularly effective on power-law graphs, as demonstrated by our extensive performance analysis. In the largest tested configuration, an R-MAT graph with $2^{38}$ vertices and $2^{42}$ edges on 32,768 Blue Gene/Q nodes, we have achieved a processing rate of three Trillion Edges Per Second (TTEPS), a four orders of magnitude improvement over the best published results.