Abstract
We propose a new parallel algorithm for the single-source shortest-path problem (SSSP). Its heap data structure is particularly advantageous on graphs with a moderate number of high degree nodes. On arbitrary directed graphs with n nodes, m edges and independent random edge weights uniformly distributed in the range [0, 1] and maximum shortest path weight L the PRAM version of our algorithm runs in O(log2 nċmini{2iċLċlog n+|Vi|}) average-case time using O(nċlog n+m) operations where |Vi| is the number of graph vertices with degree at least 2i. For power-law graph models of the Internet or call graphs this results in the first work-efficient o(n1/4) average-case time algorithm.
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