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 ε. We present a data structure that solves an approximate version of this problem: it counts all subpaths whose Fréchet distance is at most ε  , but this count may also include subpaths whose Fréchet distance is up to (2+32)ε. For any parameter n≤s≤n2n≤s≤n2, our data structure can be tuned such that it uses O(spolylogn) storage and has O((n/s)polylogn) query time.