Computing the Fréchet distance with a retractable leash

K. Buchin, M. Buchin, R. Leusden, van, W. Meulemans, W. Mulzer

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

7 Citations (Scopus)
48 Downloads (Pure)

Abstract

All known algorithms for the Fréchet distance between curves proceed in two steps: first, they construct an efficient oracle for the decision version; then they use this oracle to find the optimum among a finite set of critical values. We present a novel approach that avoids the detour through the decision version. We demonstrate its strength by presenting a quadratic time algorithm for the Fréchet distance between polygonal curves in R^d under polyhedral distance functions, including L_1 and L_infinity. We also get a (1+eps)-approximation of the Fréchet distance under the Euclidean metric. For the exact Euclidean case, our framework currently gives an algorithm with running time O(n^2 log^2 n). However, we conjecture that it may eventually lead to a faster exact algorithm.
Original languageEnglish
Title of host publication21st Annual European Symposium on Algorithms (ESA)
EditorsH.L. Bodlaender, G.F. Italiano
Place of PublicationBerlin
PublisherSpringer
Pages241-252
ISBN (Print)978-3-642-40449-8
DOIs
Publication statusPublished - 2013
Event21st Annual European Symposium on Algorithms (ESA 2013) - Sophia Antipolis, France
Duration: 2 Sep 20134 Sep 2013
Conference number: 21st
http://www.informatik.uni-trier.de/~ley/db/conf/esa/esa2013.html

Publication series

NameLecture Notes in Computer Science
Volume8125
ISSN (Print)0302-9743

Conference

Conference21st Annual European Symposium on Algorithms (ESA 2013)
Abbreviated titleESA 2013
CountryFrance
CitySophia Antipolis
Period2/09/134/09/13
Internet address

Cite this

Buchin, K., Buchin, M., Leusden, van, R., Meulemans, W., & Mulzer, W. (2013). Computing the Fréchet distance with a retractable leash. In H. L. Bodlaender, & G. F. Italiano (Eds.), 21st Annual European Symposium on Algorithms (ESA) (pp. 241-252). (Lecture Notes in Computer Science; Vol. 8125). Springer. https://doi.org/10.1007/978-3-642-40450-4_21