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 language | English |
|---|---|
| Article number | 4 |
| Pages (from-to) | 39:1-39:36 |
| Number of pages | 36 |
| Journal | ACM Transactions on Algorithms |
| Volume | 19 |
| Issue number | 4 |
| DOIs | |
| 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 |
Bibliographical note
DBLP License: DBLP's bibliographic metadata records provided through http://dblp.org/ are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.Keywords
- Fréchet distance
- distance oracle
- high dimension
- simplification
- streaming algorithm
- the "zoom in" problem