@MISC{Meyer02designand, author = {Ulrich Meyer}, title = {Design and Analysis of Sequential . . . }, year = {2002} }

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Abstract

We study the performance of algorithms for the Single-Source Shortest-Paths (SSSP) problem on graphs withÒnodes andÑedges with nonnegative random weights. All previously known SSSP algorithms for directed graphs required superlinear time. We give the first SSSP algorithms that provably achieve linearÇÒÑaverage-case execution time on arbitrary directed graphs with random edge weights. For independent edge weights, the linear-time bound holds with high probability, too. Additionally, our result implies improved average-case bounds for the All-Pairs Shortest-Paths (APSP) problem on sparse graphs, and it yields the first theoretical average-case analysis for the “Approximate Bucket Implementation” of Dijkstra’s SSSP algorithm (ABI–Dijkstra). Furthermore, we give constructive proofs for the existence of graph classes with random edge weights on which ABI–Dijkstra and several other well-known SSSP algorithms require superlinear averagecase time. Besides the classical sequential (single processor) model of computation we also consider parallel computing: we give the currently fastest average-case linear-work parallel SSSP algorithms for large graph classes with random edge weights, e.g., sparse random graphs and graphs modeling the WWW, telephone calls or social networks.