An Approximate Algorithm for Solving the Watchman Route Problem

The watchman route problem (WRP) was first introduced in 1988 and is defined as follows: How to calculate a shortest route completely contained inside a simple polygon such that any point inside this polygon is visible from at least one point on the route? So far the best known result for the WRP is an O(n(3) log n) runtime algorithm (with inherent numerical problems of its implementation). This paper gives an k(epsilon) x O(kn) approximate algorithm for WRP by using a rubberband algorithm, where n is the number of vertices of the simple polygon, k the number of essential cuts, epsilon the chosen accuracy constant for the minimization of the calculated route, and k(epsilon) equals the length of the initial route minus the length of the calculated route, divided by epsilon.

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