Multiple Watchman Routes in Staircase Polygons
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918080273186816 |
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| author | Brötzner, Anna Nilsson, Bengt J. Schmidt, Christiane |
| author_facet | Brötzner, Anna Nilsson, Bengt J. Schmidt, Christiane |
| contents | We consider the watchman route problem for multiple watchmen in staircase polygons, which are rectilinear $x$- and $y$-monotone polygons. For two watchmen, we propose an algorithm to find an optimal solution that takes quadratic time, improving on the cubic time of a trivial solution. For $m \geq 3$ watchmen, we explain where this approach fails, and present an approximation algorithm for the min-max criterion with only an additive error. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01940 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multiple Watchman Routes in Staircase Polygons Brötzner, Anna Nilsson, Bengt J. Schmidt, Christiane Computational Geometry We consider the watchman route problem for multiple watchmen in staircase polygons, which are rectilinear $x$- and $y$-monotone polygons. For two watchmen, we propose an algorithm to find an optimal solution that takes quadratic time, improving on the cubic time of a trivial solution. For $m \geq 3$ watchmen, we explain where this approach fails, and present an approximation algorithm for the min-max criterion with only an additive error. |
| title | Multiple Watchman Routes in Staircase Polygons |
| topic | Computational Geometry |
| url | https://arxiv.org/abs/2507.01940 |