Improved Algorithms for Partial Curve Matching

  • Anil Maheshwari
  • Jörg-Rüdiger Sack
  • Kaveh Shahbaz
  • Hamid Zarrabi-Zadeh
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6942)

Abstract

Back in 1995, Alt and Godau gave an efficient algorithm for deciding whether a given curve resembles some part of a larger curve under a fixed Fréchet distance, achieving a running time of O(nm log(nm)), for n and m being the number of segments in the two curves, respectively. We improve this long-standing result by presenting an algorithm that solves this decision problem in O(nm) time. 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 case when the map is a directed acyclic graph.

Keywords

Directed Acyclic Graph Query Point Improve Algorithm Partial Curve Maximum Walk 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

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

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