Sweeping $x$-monotone pseudolines
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913964195053568 |
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| author | Biedl, Therese Chambers, Erin Kostitsyna, Irina Rote, Günter |
| author_facet | Biedl, Therese Chambers, Erin Kostitsyna, Irina Rote, Günter |
| contents | We study the problem of sweeping a pseudoline arrangement with $n$ $x$-monotone curves with a rope (an $x$-monotone curve that connects the points at infinity). The rope can move by flipping over a face of the arrangement, replacing parts of it from the lower to the upper chain of the face. Counting as length of the rope the number of edges, what rope-length can be needed in such a sweep? We show that all such arrangements can be swept with rope-length at most $2n-2$, and for some arrangements rope-length at least $7(n-2)/4+1$ is required. We also discuss some complexity issues around the problem of computing a sweep with the shortest rope-length. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_21322 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sweeping $x$-monotone pseudolines Biedl, Therese Chambers, Erin Kostitsyna, Irina Rote, Günter Computational Geometry We study the problem of sweeping a pseudoline arrangement with $n$ $x$-monotone curves with a rope (an $x$-monotone curve that connects the points at infinity). The rope can move by flipping over a face of the arrangement, replacing parts of it from the lower to the upper chain of the face. Counting as length of the rope the number of edges, what rope-length can be needed in such a sweep? We show that all such arrangements can be swept with rope-length at most $2n-2$, and for some arrangements rope-length at least $7(n-2)/4+1$ is required. We also discuss some complexity issues around the problem of computing a sweep with the shortest rope-length. |
| title | Sweeping $x$-monotone pseudolines |
| topic | Computational Geometry |
| url | https://arxiv.org/abs/2507.21322 |