TY - GEN

T1 - Static and streaming data structures for Fréchet distance queries

AU - Filtser, Arnold

AU - Filtser, Omrit

N1 - Publisher Copyright:
Copyright © 2021 by SIAM

PY - 2021/1/1

Y1 - 2021/1/1

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 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=85105269438&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:85105269438

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 1150

EP - 1170

BT - ACM-SIAM Symposium on Discrete Algorithms, SODA 2021

A2 - Marx, Daniel

PB - Association for Computing Machinery

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

Y2 - 10 January 2021 through 13 January 2021

ER -