Optimum Sweeps of Simple Polygons with Two Guards
A polygon P admits a sweep if two mobile guards can detect an unpredictable, moving target inside P, no matter how fast the target moves. For safety, two guards are required to always be mutually visible, and thus, they should move on the polygon boundary. Our objective in this paper is to find an optimum sweep such that the sum of the distances travelled by the two guards in the sweep is minimized. We present an O(n 2) time and O(n) space algorithm, where n is the number of vertices of the given polygon. This new result is obtained by converting the problem of sweeping simple polygons with two guards into that of finding a shortest path between two nodes in a graph of size O(n).
KeywordsBasic Motion Linear Time Algorithm Simple Polygon Polygon Boundary Clear Region
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