Optimization Algorithms for Sweeping a Polygonal Region with Mobile Guards
Abstract

 Given an nsided polygon, we present an O(n^{2} log n)time algorithm for computing a shortest walk in which the total length of the paths that two guards traverse is minimized.

 Given an nsided polygon, we present an O(n^{2})time algorithm for computing a minimum diameter walk in which the maximum distance between two guards is minimized.
Finally we allow more than two guards. Here the guards should form a simple chain within the polygon such that any consecutive two guards along the chain are mutually visible and the first and last guard have to move along the boundary but others do not.  We present an O(n^{2})time algorithm for computing the minimum number of guards to sweep an nsided polygon and an O(n^{3})time algorithm for computing such a schedule.
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