Jaywalking your dog: Computing the Fréchet distance with shortcuts

A. Driemel, S. Har-Peled

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

12 Citations (Scopus)

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(c^2 kn log^3 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(c^2 n log^3 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.
Original languageEnglish
Title of host publicationProceedings of the 23rd Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'12),17-19 january 2012, Kyoto, Japan
EditorsY. Rabani
PublisherSociety for Industrial and Applied Mathematics (SIAM)
Pages318-327
ISBN (Print)978-1-61197-210-8
DOIs
Publication statusPublished - 2012
Externally publishedYes
Event23rd Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2012) - Westin Miyako, Kyoto, Japan
Duration: 17 Jan 201219 Jan 2012
Conference number: 23
http://www.siam.org/meetings/da12/

Conference

Conference23rd Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2012)
Abbreviated titleSODA '12
CountryJapan
CityKyoto
Period17/01/1219/01/12
Internet address

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