Approximation Algorithms for the Watchman Route and Zookeeper’s Problems

Abstract

Given a simple polygon P with n vertices and a starting point s on its boundary, the watchman route problem asks for a shortest route in P through s such that each point in the interior of the polygon can be seen from at least one point along the route.It is known that the watchman route problem can be reduced in O (n log n )time to that of computing the shortest route which visits a set of line segments in polygon P .In this paper,we present a simple approximation algorithm for computing the shortest route visiting that set of line segments. Our algorithm runs in O(n)time and produces a watchman route of at most 2 times the length of the shortest watchman route.The best known algorithm for computing the shortest watchman through s takes O(n ⁴)time [3]. Our scheme is also employed to give a √2-approximation solution to the zookeeper’s problem, which is a variant of the watchman route problem.