Discrete & Computational Geometry

, Volume 48, Issue 1, pp 94–127 | Cite as

Approximating the Fréchet Distance for Realistic Curves in Near Linear Time



We present a simple and practical (1+ε)-approximation algorithm for the Fréchet distance between two polygonal curves in ℝd. To analyze this algorithm we introduce a new realistic family of curves, c-packed curves, that is closed under simplification. We believe the notion of c-packed curves to be of independent interest. We show that our algorithm has near linear running time for c-packed polygonal curves, and similar results for other input models, such as low-density polygonal curves.


Frechet distance Approximation algorithms Realistic input models 


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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Information and Computing SciencesUtrecht UniversityUtrechtThe Netherlands
  2. 2.Department of Computer ScienceUniversity of IllinoisUrbanaUSA
  3. 3.Department of Computer ScienceUniversity of Texas at San AntonioSan AntonioUSA

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