Abstract

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(log 2 n min i f2 i L + jV i jg) average-case time using O(n+m+T ) work on a PRAM where L denotes the maximum shortest-path weight and jV i j is the number of graph vertices with in-degree at least 2 i . 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 allows adaptation to distributed memory machines, too.

Citations