Computing multiple watchman routes

Abstract

We present heuristics for computing multiple watchman routes. Given a polygon (with or without holes) and a parameter k, we compute a set of k routes inside the polygon such that any point inside the polygon is visible from at least one point along one route. We measure the quality of our solutions by either the length of the longest route or the sum of the route lengths, where the goal is to minimize each. We start by computing a set of static guards [2], construct k routes that visit all the static guards and try to shorten the routes while maintaining full coverage of the polygon. We implemented the algorithm and present extensive results to evaluate our methods, including a comparison with lower bound routes based on the idea of visiting large number of visibility-independent "witness points". Our experiments showed that for a large suite of input data our heuristics give efficient routes that are comparable with the optimal solutions. © 2008 Springer-Verlag Berlin Heidelberg.