Static and streaming data structures for Fréchet distance queries

Arnold Filtser, Omrit Filtser

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

Abstract

Given a curve P with points in Rd in a streaming fashion, and parameters ε > 0 and k, we construct a distance oracle that uses O(1ε)kd log ε1 space, and given a query curve Q with k points in Rd, returns in Õ(kd) time a 1 + ε approximation of the discrete Fréchet distance between Q and P. In addition, we construct simplifications in the streaming model, oracle for distance queries to a sub-curve (in the static setting), and introduce the zoom-in problem. Our algorithms work in any dimension d, and therefore we generalize some useful tools and algorithms for curves under the discrete Fréchet distance to work efficiently in high dimensions.

Original languageEnglish
Title of host publicationACM-SIAM Symposium on Discrete Algorithms, SODA 2021
EditorsDaniel Marx
PublisherAssociation for Computing Machinery
Pages1150-1170
Number of pages21
ISBN (Electronic)9781611976465
StatePublished - 2021
Externally publishedYes
Event32nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2021 - Alexandria, Virtual, United States
Duration: 10 Jan 202113 Jan 2021

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Conference

Conference32nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2021
Country/TerritoryUnited States
CityAlexandria, Virtual
Period10/01/2113/01/21

Bibliographical note

Publisher Copyright:
Copyright © 2021 by SIAM

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