Name
Abstract | ||
|---|---|---|
The Frechet distance is a popular and widespread distance measure for point sequences and for curves. About two years ago, Agarwal et al. [SIAM J. Comput. 2014] presented a new (mildly) subquadratic algorithm for the discrete version of the problem. This spawned a flurry of activity that has led to several new algorithms and lower bounds.In this paper, we study the approximability of the discrete Frechet distance. Building on a recent result by Bringmann [FOCS 2014], we present a new conditional lower bound showing that strongly subquadratic algorithms for the discrete Frechet distance are unlikely to exist, even in the one-dimensional case and even if the solution may be approximated up to a factor of 1.399.This raises the question of how well we can approximate the Frechet distance (of two given d-dimensional point sequences of length n) in strongly subquadratic time. Previously, no general results were known. We present the first such algorithm by analysing the approximation ratio of a simple, linear-time greedy algorithm to be 2(Theta(n)). Moreover, we design an alpha-approximation algorithm that runs in time O(n log n + n(2)/alpha), for any alpha is an element of[1, n]. Hence, an n(epsilon)-approximation of the Frechet distance can be computed in strongly subquadratic time, for any epsilon > 0. |
Year | Venue | Field |
|---|---|---|
2016 | JOURNAL OF COMPUTATIONAL GEOMETRY | Topology,Binary logarithm,Discrete mathematics,Combinatorics,Upper and lower bounds,Greedy algorithm,Fréchet distance,Mathematics |
DocType | Volume | Issue |
Journal | 7 | 2 |
ISSN | Citations | PageRank |
1920-180X | 7 | 0.54 |
References | Authors | |
11 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Karl Bringmann | 1 | 427 | 30.13 |
| Wolfgang Mulzer | 2 | 257 | 36.08 |