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Approximate Shortest Path Queries Using Voronoi Duals

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Book cover Transactions on Computational Science IX

Part of the book series: Lecture Notes in Computer Science ((TCOMPUTATSCIE,volume 6290))

Abstract

We propose an approximation method to answer point-to-point shortest path queries in undirected edge-weighted graphs, based on random sampling and Voronoi duals. We compute a simplification of the graph by selecting nodes independently at random with probability p. Edges are generated as the Voronoi dual of the original graph, using the selected nodes as Voronoi sites. This overlay graph allows for fast computation of approximate shortest paths for general, undirected graphs. The time–quality tradeoff decision can be made at query time. We provide bounds on the approximation ratio of the path lengths as well as experimental results. The theoretical worst-case approximation ratio is bounded by a logarithmic factor. Experiments show that our approximation method based on Voronoi duals has extremely fast preprocessing time and efficiently computes reasonably short paths.

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Authors and Affiliations

  1. National Institute of Informatics, Tokyo, Japan

    Shinichi Honiden, Michael E. Houle, Christian Sommer & Martin Wolff

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  1. Shinichi Honiden
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  2. Michael E. Houle
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  3. Christian Sommer
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  4. Martin Wolff
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Editors and Affiliations

  1. Department of Computer Science, University of Calgary, 2500 University Drive N.W., T2N 1N4, Calgary, AB, Canada

    Marina L. Gavrilova

  2. Exascala Ltd., Unit 9, 97 Rickman Drive, B15 2AL, Birmingham, UK

    C. J. Kenneth Tan

  3. Department of Informatics and Mathematical Modeling, Technical University of Denmark, Richard Petersens Plads, 2800, Lyngby, Denmark

    François Anton

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Honiden, S., Houle, M.E., Sommer, C., Wolff, M. (2010). Approximate Shortest Path Queries Using Voronoi Duals. In: Gavrilova, M.L., Tan, C.J.K., Anton, F. (eds) Transactions on Computational Science IX. Lecture Notes in Computer Science, vol 6290. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16007-3_2

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  • DOI: https://doi.org/10.1007/978-3-642-16007-3_2

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