A near-linear time exact algorithm for the $L_1$-geodesic Fréchet distance between two curves on the boundary of a simple polygon
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912334301102080 |
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| author | van der Horst, Thijs van Kreveld, Marc Ophelders, Tim Speckmann, Bettina |
| author_facet | van der Horst, Thijs van Kreveld, Marc Ophelders, Tim Speckmann, Bettina |
| contents | 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 $\mathcal{O}(k \log nm + (n+m) (\log^2 nm \log k + \log^4 nm))$ time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_13704 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A near-linear time exact algorithm for the $L_1$-geodesic Fréchet distance between two curves on the boundary of a simple polygon van der Horst, Thijs van Kreveld, Marc Ophelders, Tim Speckmann, Bettina Computational Geometry F.2.2 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 $\mathcal{O}(k \log nm + (n+m) (\log^2 nm \log k + \log^4 nm))$ time. |
| title | A near-linear time exact algorithm for the $L_1$-geodesic Fréchet distance between two curves on the boundary of a simple polygon |
| topic | Computational Geometry F.2.2 |
| url | https://arxiv.org/abs/2504.13704 |