Buckets strike back: improved parallel shortest-paths

We study the average-case complexity of the parallel single-source shortest path (SSSP) problem, assuming arbitrary directed graphs with n nodes, m edges, and independent random edge weights uniformly distributed in [0, 1]. We provide a new bucket-based parallel SSSP algorithm that runs in T=O(log² n·min_i{2ⁱ·L+|V_i|}) average-case time using O(n+m+T) work on a PRAM, where L denotes the maximum shortest-path weight and |V_i| is the number of graph vertices with in-degree at least 2ⁱ. All previous algorithms either required more time or more work. The minimum performance gain is a logarithmic factor improvement; on certain graph classes, accelerations by factors of more than n^0.4 can be achieved. The algorithm also allows adaptation to distributed memory machines.