A linear-time 2-approximation algorithm for the watchman route problem for simple polygons

Given a simple polygon P of n vertices, the watchman route problem asks for a shortest (closed) route inside P such that each point in the interior of P can be seen from at least one point along the route. In this paper, we present a simple, linear-time algorithm for computing a watchman route of length at most two times that of the shortest watchman route. The best known algorithm for computing a shortest watchman route takes 0 (n(4) log n) time, which is too complicated to be suitable in practice. This paper also involves an optimal 0 (n) time algorithm for computing the set of so-called essential cuts, which are the line segments inside the polygon P such that any route visiting them is a watchman route. It solves an intriguing open problem by improving the previous 0 (n log n) time result, and is thus of interest in its own right. (c) 2007 Elsevier B.V. All rights reserved.