Fast Frechet Queries

Inspired by video analysis of team sports, we study the following problem. Let P be a polygonal path in the plane with n vertices. We want to preprocess P into a data structure that can quickly count the number of inclusion-minimal subpaths of P whose Frechet distance to a given query segment Q is at most some threshold value epsilon. We present a data structure that solves an approximate version of this problem: it counts all subpaths whose Frechet distance is at most epsilon, but this count may also include subpaths whose Frechet distance is up to (2+3 root 2)epsilon. For any parameter n <= s <= n(2), our data structure can be tuned such that it uses O (s polylogn) storage and has O ((n/root S) polylogn) query time. Crown Copyright (C) 2012 Published by Elsevier B.V. All rights reserved.