Multiple Watchman Routes in Staircase Polygons

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