A Linear-time Algorithm for Orthogonal Watchman Route Problem with Minimum Bends

TL;DR

This paper introduces a linear-time algorithm for solving the orthogonal watchman route problem in monotone polygons, optimizing for minimal bends and applicable to certain path polygons.

Contribution

It presents the first linear-time solution for the orthogonal watchman route problem in monotone polygons, focusing on minimizing route bends.

Findings

Algorithm runs in linear time for monotone polygons.

Effective in minimizing the number of bends in the route.

Applicable to path polygons with a specific dual graph structure.

Abstract

Given an orthogonal polygon $ P $ with $ n $ vertices, the goal of the watchman route problem is finding a path $ S $ of the minimum length in $ P $ such that every point of the polygon $ P $ is visible from at least one of the point of $ S $. In the other words, in the watchman route problem we must compute a shortest watchman route inside a simple polygon of $ n $ vertices such that all the points interior to the polygon and on its boundary are visible to at least one point on the route. If route and polygon be orthogonal, it is called orthogonal watchman route problem. One of the targets of this problem is finding the orthogonal path with the minimum number of bends as possible. We present a linear-time algorithm for the orthogonal watchman route problem, in which the given polygon is monotone. Our algorithm can be used also for the problem on simple orthogonal polygons $ P $ for which the dual graph induced by the vertical decomposition of $ P $ is a path, which is called path polygon.