An Approximate Algorithm for Solving the Watchman Route Problem
نویسندگان
چکیده
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(nlogn) runtime algorithm (with inherent numerical problems of its implementation). This paper gives an κ(ε) × O(kn) approximate algorithm for WRP by using a rubberband algorithm, where n is the number of vertices of the simple polygon, k a number of essential cuts and ε the chosen accuracy constant.
منابع مشابه
Watchman route in a simple polygon with a rubberband algorithm
So far, the best result in running time for solving the fixed watchman route problem (i.e., shortest path for viewing any point in a simple polygon with given start point) is O(n log n), published in 2003 by M. Dror, A. Efrat, A. Lubiw, and J. Mitchell. – This paper provides an algorithm with κ(ε) · O(kn) runtime, where n is the number of vertices of the given simple polygon Π, and k the number...
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