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A fully dynamic approximation scheme for all-pairs shortest paths in planar graphs

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Algorithms and Data Structures (WADS 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 709))

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Abstract

In this paper we give a fully dynamic approximation scheme for maintaining all-pairs shortest paths in planar networks. Given an error parameter ε such that 0<ε≤1, our algorithm maintains approximate allpairs shortest-paths in an undirected planar graph G with nonnegative edge lengths. The approximate paths are guaranteed to be accurate to within a (1+ε)-factor. The time bounds for both query and update for our algorithm wis O(ε −1 n 2/3 log2 n log D), where n is the number of nodes in G and D is the sum of its edge lengths.

Our approximation algorithm is based upon a novel technique for approximately representing all-pairs shortest paths among a selected subset of the nodes by a sparse substitute graph.

Research supported by NSF grant CCR-9012357 and NSF PYI award CCR-9157620, together with PYI matching funds from Thinking Machines Corporation and Xerox Corporation. Additional support provided by DARPA contract N00014-91-J-4052 ARPA Order 8225.

Research supported in part by a National Science Foundation Presidential Young Investigator Award CCR-9047466 with matching funds from IBM, by NSF research grant CCR-9007851, by Army Research Office grant DAAL03-91-G-0035, and by the Office of Naval Research and the Defense Advanced Research Projects Agency under contract N00014-91-J-4052 and ARPA order 8225.

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Authors and Affiliations

  1. Department of Computer Science, Brown University, 02912, Providence, R. I., USA

    Philip N. Klein & Sairam Subramanian

Authors
  1. Philip N. Klein
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  2. Sairam Subramanian
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Editor information

Frank Dehne Jörg-Rüdiger Sack Nicola Santoro Sue Whitesides

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© 1993 Springer-Verlag Berlin Heidelberg

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Klein, P.N., Subramanian, S. (1993). A fully dynamic approximation scheme for all-pairs shortest paths in planar graphs. In: Dehne, F., Sack, JR., Santoro, N., Whitesides, S. (eds) Algorithms and Data Structures. WADS 1993. Lecture Notes in Computer Science, vol 709. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57155-8_269

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  • DOI: https://doi.org/10.1007/3-540-57155-8_269

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57155-1

  • Online ISBN: 978-3-540-47918-5

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