Static and Streaming Data Structures for Fréchet Distance Queries

Research output: Contribution to journalArticlepeer-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 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.

Original languageEnglish
Article number4
Pages (from-to)39:1-39:36
Number of pages36
JournalACM Transactions on Algorithms
Volume19
Issue number4
DOIs
StatePublished - 25 Oct 2023
Event32nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2021 - Alexandria, Virtual, United States
Duration: 10 Jan 202113 Jan 2021

Keywords

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

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)

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