ISAAC 2001: Algorithms and Computation pp 480-492

# Optimization Algorithms for Sweeping a Polygonal Region with Mobile Guards

• Jae-Ha Lee
• Sang-Min Park
• Kyung-Yong Chwa
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2223)

## Abstract

We study the problem of sweeping a simple polygon using a chain of mobile guards. The basic question is as follows:Given a simple polygon P in the plane, is it possible for two guards to simultaneously walk along the boundary of P from one point to another point in such a way that two guards are always mutually visible and any target moving continuously inside P should eventually lie on the line segment between two guards? It is known that an O(n2)-time algorithm can decide this question. Our contribution is to present efficient algorithms for the following optimization problems:
• - Given an n-sided polygon, we present an O(n2 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 n-sided polygon, we present an O(n2)-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(n2)-time algorithm for computing the minimum number of guards to sweep an n-sided polygon and an O(n3)-time algorithm for computing such a schedule.

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