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

  • Philip N. Klein
  • Sairam Subramanian
Conference paper

DOI: 10.1007/3-540-57155-8_269

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

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−1n2/3 log2n 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.

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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Philip N. Klein
    • 1
  • Sairam Subramanian
    • 1
  1. 1.Department of Computer ScienceBrown UniversityProvidenceUSA

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