Min-Max Multiple Fixed Watchman Routes in Minbar Polygons, with Non-domination Assumption

In this paper, the problem of multiple watchman routes in Minbar polygons\footnote{A minbar is a pulpit in a mosque where the imam (leader of prayers) stands to deliver sermons.} is studied, where every point in the given polygon must be visible from at least one point on some watchmen's route. The problem of multiple watchman routes is NP-hard even in simple polygons. However, some limited types of polygon have been shown to have polynomial-time solutions. We propose an algorithm based on the dynamic programming approach that requires \( O(n) \) space and consumes \( O(n \cdot \log(n)) \) time for min-max criterion, where \( n \) is the number of polygon vertices. We assume that the starting points of watchmen do not dominate each-other.