Concerning the time bounds of existing shortest watchman route algorithms
A watchman route in a polygon P is a route inside P such that each point in the interior of P is visible from at least one point along the route. The objective of the shortest watchman route problem is to minimize the length of the watchman route for a given polygon. In 1991 Chin and Ntafos claimed an O(n4) algorithm, solving the shortest watchman route problem for simple polygons, given a starting point of the route. Later, improvements of this result were presented by Tan, Hirata and Inagaki, decreasing the time-bound to O(n2). We prove that the time bound analyses of these algorithms are erroneous and that their true time bound is Ω(2n). Furthermore, a modification to the latest algorithm is given, restoring its time bound to O(n2).
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