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arXiv · 2507.01940

Multiple Watchman Routes in Staircase Polygons

Anna Brötzner·Bengt J. Nilsson·Christiane Schmidt
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Abstract

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.

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Anna Brötzner, Bengt J. Nilsson, Christiane Schmidt. 2025-07-02. Multiple Watchman Routes in Staircase Polygons. https://arxiv.org/abs/2507.01940

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