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.
Cite
@article{arxiv.2507.01940,
title = {Multiple Watchman Routes in Staircase Polygons},
author = {Anna Brötzner and Bengt J. Nilsson and Christiane Schmidt},
journal= {arXiv preprint arXiv:2507.01940},
year = {2025}
}