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arXiv · 2504.13704

A near-linear time exact algorithm for the $L_1$-geodesic Fr\'echet distance between two curves on the boundary of a simple polygon

Thijs van der Horst·Marc van Kreveld·Tim Ophelders·Bettina Speckmann
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Abstract

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 Fr\'echet distance between $R$ and $B$ using the geodesic $L_1$-distance in $P$ in $\mathcal{O}(k \log nm + (n+m) (\log^2 nm \log k + \log^4 nm))$ time.

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Thijs van der Horst, Marc van Kreveld, Tim Ophelders, Bettina Speckmann. 2025-04-18. A near-linear time exact algorithm for the $L_1$-geodesic Fr\'echet distance between two curves on the boundary of a simple polygon. https://arxiv.org/abs/2504.13704

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