A near-linear time exact algorithm for the \(L_1\)-geodesic Fréchet distance between two curves on the boundary of a simple polygon
DOI:
https://doi.org/10.57717/cgt.v5i1.114Abstract
Let \(P\) be a polygon with \(k\)vertices. Let \(R\) and \(B\) be two simple, interior disjoint curves on the boundary of \(P\), with \(n\) and \(m\) vertices. We show how to compute the Fréchet distance between \(R\) and \(B\) using the geodesic \(L_1\)-distance in \(P\) in \(O(k \log nm + (n+m) (\log^2 nm \log k + \log^4 nm))\) time.
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Copyright (c) 2022 Thijs van der Horst, Marc van Kreveld, Tim Ophelders, Bettina Speckmann
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