Static and Streaming Data Structures for Fréchet Distance Queries

Arnold Filtser; Omrit Filtser

doi:10.1145/3610227

Static and Streaming Data Structures for Fréchet Distance Queries

Arnold Filtser, Omrit Filtser

Bar-Ilan University, Open University of Israel

Research output: Contribution to journal › Article › 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 space, and given a query curve Q with k points in ℝ^d returns in 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
Article number	39
Pages (from-to)	39:1-39:36
Number of pages	36
Journal	ACM Transactions on Algorithms
Volume	19
Issue number	4
DOIs	https://doi.org/10.1145/3610227
State	Published - 25 Oct 2023
Event	32nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2021 - Alexandria, Virtual, United States Duration: 10 Jan 2021 → 13 Jan 2021

Keywords

Fréchet distance
distance oracle
high dimension
simplification
streaming algorithm
the "zoom in" problem

All Science Journal Classification (ASJC) codes

Mathematics (miscellaneous)

Access to Document

10.1145/3610227

Cite this

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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 space, and given a query curve Q with k points in ℝd returns in 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.",

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AU - Filtser, Omrit

PY - 2023/10/25

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N2 - 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 space, and given a query curve Q with k points in ℝd returns in 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.

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 space, and given a query curve Q with k points in ℝd returns in 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.

KW - Fréchet distance

KW - distance oracle

KW - high dimension

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T2 - 32nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2021

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Static and Streaming Data Structures for Fréchet Distance Queries

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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