Algorithmica

, Volume 69, Issue 3, pp 641–657 | Cite as

Improved Algorithms for Partial Curve Matching

  • Anil Maheshwari
  • Jörg-Rüdiger Sack
  • Kaveh Shahbaz
  • Hamid Zarrabi-Zadeh
Article

Abstract

We revisit the problem of deciding whether a given curve resembles some part of a larger curve under a fixed Fréchet distance, achieving a running time of O(nm), for n and m being the number of segments in the two curves. This improves the long-standing result of Alt and Godau by an O(log(nm)) factor. Our solution is based on constructing a simple data structure which we call free-space map. Using this data structure, we obtain improved algorithms for several variants of the Fréchet distance problem, including the Fréchet distance between two closed curves, and the so-called minimum/maximum walk problems. We also improve the map matching algorithm of Alt et al. for the particular case in which the map is a directed acyclic graph.

Keywords

Fréchet distance Partial curve matching Closed curves Free-space map 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Anil Maheshwari
    • 1
  • Jörg-Rüdiger Sack
    • 1
  • Kaveh Shahbaz
    • 1
  • Hamid Zarrabi-Zadeh
    • 2
  1. 1.School of Computer ScienceCarleton UniversityOttawaCanada
  2. 2.Department of Computer EngineeringSharif University of TechnologyTehranIran

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