research-article

Jaywalking your dog: computing the Fréchet distance with shortcuts

Authors:

Sariel Har-PeledAuthors Info & Claims

SODA '12: Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete algorithms

Pages 318 - 337

Published: 17 January 2012 Publication History

Abstract

The similarity of two polygonal curves can be measured using the Fréchet distance. We introduce the notion of a more robust Fréchet distance, where one is allowed to shortcut between vertices of one of the curves. This is a natural approach for handling noise, in particular batched outliers. We compute a constant factor approximation to the minimum Fréchet distance over all possible such shortcuts. Our algorithm runs in O(c² kn log³ n) time if one is allowed to take at most k shortcuts and the input curves are c-packed. For the case where the number of shortcuts is unrestricted, we describe an algorithm which runs in O(c² n log³ n) time. To facilitate the new algorithm we develop several new data-structures, which we believe to be of independent interest: (i) for range reporting on a curve, and (ii) for preprocessing a curve to answer queries for the Fréchet distance between a subcurve and a line segment.

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Cited By

Buchin KBuchin MMeulemans WMulzer WChekuri C(2014)Four soviets walk the dogProceedings of the twenty-fifth annual ACM-SIAM symposium on Discrete algorithms10.5555/2634074.2634177(1399-1413)Online publication date: 5-Jan-2014
https://dl.acm.org/doi/10.5555/2634074.2634177
Buchin MDriemel ASpeckmann BCheng SDevillers O(2014)Computing the Fréchet distance with shortcuts is NP-hardProceedings of the thirtieth annual symposium on Computational geometry10.1145/2582112.2582144(367-376)Online publication date: 8-Jun-2014
https://dl.acm.org/doi/10.1145/2582112.2582144
Agarwal PAvraham RKaplan HSharir MKhanna S(2013)Computing the discrete Fréchet distance in subquadratic timeProceedings of the twenty-fourth annual ACM-SIAM symposium on Discrete algorithms10.5555/2627817.2627829(156-167)Online publication date: 6-Jan-2013
https://dl.acm.org/doi/10.5555/2627817.2627829
Show More Cited By

Index Terms

Jaywalking your dog: computing the Fréchet distance with shortcuts
1. Mathematics of computing
  1. Discrete mathematics
2. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

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cover image ACM Other conferences

SODA '12: Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete algorithms

January 2012

1764 pages

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Kyoto University: Kyoto University

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SIGACT: ACM Special Interest Group on Algorithms and Computation Theory

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Society for Industrial and Applied Mathematics

United States

Publication History

Published: 17 January 2012

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SODA '12

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Kyoto University

SODA '12: ACM-SIAM Symposium on Discrete Algorithms

January 17 - 19, 2012

Kyoto, Japan

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Overall Acceptance Rate 411 of 1,322 submissions, 31%

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Cited By

Buchin KBuchin MMeulemans WMulzer WChekuri C(2014)Four soviets walk the dogProceedings of the twenty-fifth annual ACM-SIAM symposium on Discrete algorithms10.5555/2634074.2634177(1399-1413)Online publication date: 5-Jan-2014
https://dl.acm.org/doi/10.5555/2634074.2634177
Buchin MDriemel ASpeckmann BCheng SDevillers O(2014)Computing the Fréchet distance with shortcuts is NP-hardProceedings of the thirtieth annual symposium on Computational geometry10.1145/2582112.2582144(367-376)Online publication date: 8-Jun-2014
https://dl.acm.org/doi/10.1145/2582112.2582144
Agarwal PAvraham RKaplan HSharir MKhanna S(2013)Computing the discrete Fréchet distance in subquadratic timeProceedings of the twenty-fourth annual ACM-SIAM symposium on Discrete algorithms10.5555/2627817.2627829(156-167)Online publication date: 6-Jan-2013
https://dl.acm.org/doi/10.5555/2627817.2627829
Chambers EWang Yda Fonseca GLewiner TPeñaranda LChan TKlein R(2013)Measuring similarity between curves on 2-manifolds via homotopy areaProceedings of the twenty-ninth annual symposium on Computational geometry10.1145/2462356.2462375(425-434)Online publication date: 17-Jun-2013
https://dl.acm.org/doi/10.1145/2462356.2462375
De Berg MCook AGudmundsson J(2013)Fast Fréchet queriesComputational Geometry: Theory and Applications10.1016/j.comgeo.2012.11.00646:6(747-755)Online publication date: 1-Aug-2013
https://dl.acm.org/doi/10.1016/j.comgeo.2012.11.006

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