Abstract
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 \((2+3\sqrt{2})\varepsilon \). For any parameter n ≤ s ≤ n 2, our data structure can be tuned such that it uses O(s polylog n) storage and has \(O((n/\sqrt{s}){\rm polylog} n)\) query time. For the special case where we wish to count all subpaths whose Fréchet Distance to Q is at most ε·length(Q), we present a structure with O(n polylog n) storage and O(polylog n) query time.
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de Berg, M., Cook, A.F., Gudmundsson, J. (2011). Fast Fréchet Queries. In: Asano, T., Nakano, Si., Okamoto, Y., Watanabe, O. (eds) Algorithms and Computation. ISAAC 2011. Lecture Notes in Computer Science, vol 7074. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25591-5_26
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DOI: https://doi.org/10.1007/978-3-642-25591-5_26
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