Finding the Shortest Watchman Route in a Simple Polygon

Abstract. We present the first polynomial time algorithm that finds the shortest route in a simple polygon such that all points of the polygon are visible from the route. This route is called the shortest watchman route, and we do not assume any restrictions on the route or on the simple polygon. Our algorithm runs in worst case O(n6) time, but it is adaptive, making it run faster on polygons with a simple structure.

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