Computing the Fréchet Distance with a Retractable Leash

  • Kevin Buchin
  • Maike Buchin
  • Rolf van Leusden
  • Wouter Meulemans
  • Wolfgang Mulzer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8125)

Abstract

All known algorithms for the Fréchet distance between curves proceed in two steps: first, they construct an efficient oracle for the decision version; then they use this oracle to find the optimum among a finite set of critical values. We present a novel approach that avoids the detour through the decision version. We demonstrate its strength by presenting a quadratic time algorithm for the Fréchet distance between polygonal curves in ℝd under polyhedral distance functions, including L1 and L ∞ . We also get a (1 + ε)-approximation of the Fréchet distance under the Euclidean metric. For the exact Euclidean case, our framework currently gives an algorithm with running time O(n2 log2n). However, we conjecture that it may eventually lead to a faster exact algorithm.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Kevin Buchin
    • 1
  • Maike Buchin
    • 2
  • Rolf van Leusden
    • 1
  • Wouter Meulemans
    • 1
  • Wolfgang Mulzer
    • 3
  1. 1.Technical University EindhovenThe Netherlands
  2. 2.Ruhr Universität BochumGermany
  3. 3.Freie Universität BerlinGermany

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