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A bidirectional shortest-path algorithm with good average-case behavior

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Abstract

The two-terminal shortest-path problem asks for the shortest directed path from a specified nodes to a specified noded in a complete directed graphG onn nodes, where each edge has a nonnegative length. We show that if the length of each edge is chosen independently from the exponential distribution, and adjacency lists at each node are sorted by length, then a priority-queue implementation of Dijkstra's unidirectional search algorithm has the expected running time Θ(n logn). We present a bidirectional search algorithm that has expected running time Θ(√n logn). These results are generalized to apply to a wide class of edge-length distributions, and to sparse graphs. If adjacency lists are not sorted, bidirectional search has the expected running time Θ(a√n) on graphs of average degreea, as compared with Θ(an) for unidirectional search.

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Authors and Affiliations

  1. Department of Computer Science, University of Toronto, M5S 1A4, Toronto, Canada

    Michael Luby & Prabhakar Ragde

Authors
  1. Michael Luby
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  2. Prabhakar Ragde
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Communicated by C. K. Wong.

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Luby, M., Ragde, P. A bidirectional shortest-path algorithm with good average-case behavior. Algorithmica 4, 551–567 (1989). https://doi.org/10.1007/BF01553908

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  • DOI: https://doi.org/10.1007/BF01553908

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