Fast Fréchet 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 Fréchet Distance to a given query segment Q is at most some threshold value e. We present a data structure that solves an approximate version of this problem: it counts all subpaths whose Fréchet Distance is at most e, but this count may also include subpaths whose Fréchet Distance is up to (2+3 \sqrt 2) . For any parameter n¿=¿s¿=¿n 2, our data structure can be tuned such that it uses O(s polylog n) storage and has O((n/\sqrt) polylog n) query time. For the special case where we wish to count all subpaths whose Fréchet Distance to Q is at most e·length(Q), we present a structure with O(n polylog n) storage and O(polylog n) query time