Multiple Watchman Routes in Staircase Polygons

2025/07/02 by Anna Brötzner, Brötzner, Anna, Bengt J. Nilsson +3
Computer Science · Engineering · #Computational Geometry (cs.CG) #Computational Geometry and Mesh Generation #FOS: Computer and information sciences #Optimization and Search Problems #Vehicle Routing Optimization Methods

paper · pdf · doi:10.48550/arxiv.2507.01940

openalex publication_date 2025/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 ≥ 3 watchmen, we explain where this approach fails, and present an approximation algorithm for the min-max criterion with only an additive error.

Citations

• Approximation Algorithms for the Two-Watchman Route in a Simple Polygon
• Fast Algorithms for Finding Nearest Common Ancestors

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