Static and streaming data structures for Fréchet distance queries

Arnold Filtser; Omrit Filtser

doi:10.1137/1.9781611976465.71

Static and streaming data structures for Fréchet distance queries

Arnold Filtser
, Omrit Filtser

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Given a curve P with points in R^d in a streaming fashion, and parameters ε > 0 and k, we construct a distance oracle that uses O(¹_ε)^kd log ε⁻¹ space, and given a query curve Q with k points in R^d, 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 language	English
Title of host publication	ACM-SIAM Symposium on Discrete Algorithms, SODA 2021
Editors	Daniel Marx
Publisher	Association for Computing Machinery
Pages	1150-1170
Number of pages	21
ISBN (Electronic)	9781611976465
DOIs	https://doi.org/10.1137/1.9781611976465.71
State	Published - 2021
Externally published	Yes
Event	32nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2021 - Alexandria, Virtual, United States Duration: 10 Jan 2021 → 13 Jan 2021

Publication series

Name	Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
ISSN (Print)	1071-9040
ISSN (Electronic)	1557-9468

Conference

Conference	32nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2021
Country/Territory	United States
City	Alexandria, Virtual
Period	10/01/21 → 13/01/21

Bibliographical note

Publisher Copyright:
Copyright © 2021 by SIAM

Access to Document

10.1137/1.9781611976465.71

Cite this

@inproceedings{fa49de2d433a4ba9992440ade6789446,

title = "Static and streaming data structures for Fr{\'e}chet distance queries",

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 ε−1 space, and given a query curve Q with k points in Rd, returns in {\~O}(kd) time a 1 + ε approximation of the discrete Fr{\'e}chet 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 Fr{\'e}chet distance to work efficiently in high dimensions.",

author = "Arnold Filtser and Omrit Filtser",

note = "Publisher Copyright: Copyright {\textcopyright} 2021 by SIAM; 32nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2021 ; Conference date: 10-01-2021 Through 13-01-2021",

year = "2021",

doi = "10.1137/1.9781611976465.71",

language = "אנגלית",

series = "Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms",

publisher = "Association for Computing Machinery",

pages = "1150--1170",

editor = "Daniel Marx",

booktitle = "ACM-SIAM Symposium on Discrete Algorithms, SODA 2021",

}

Filtser, A & Filtser, O 2021, Static and streaming data structures for Fréchet distance queries. in D Marx (ed.), ACM-SIAM Symposium on Discrete Algorithms, SODA 2021. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, Association for Computing Machinery, pp. 1150-1170, 32nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2021, Alexandria, Virtual, United States, 10/01/21. https://doi.org/10.1137/1.9781611976465.71

Static and streaming data structures for Fréchet distance queries. / Filtser, Arnold; Filtser, Omrit.
ACM-SIAM Symposium on Discrete Algorithms, SODA 2021. ed. / Daniel Marx. Association for Computing Machinery, 2021. p. 1150-1170 (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - 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 ε−1 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.

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Static and streaming data structures for Fréchet distance queries

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Bibliographical note

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