Optimum sweeps of simple polygons with two guards

Authors:
Xuehou Tan;Bo Jiang
Affiliations:
School of Information Science and Technology, Tokai University, 4-1-1 Kitakaname, Hiratsuka 259-1292, Japan and School of Information Science and Technology, Dalian Maritime University, Linghai Ro ...;School of Information Science and Technology, Dalian Maritime University, Linghai Road 1, Dalian, China
Venue:
Information Processing Letters
Year:
2014

Citing 6
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Optimal Algorithms for Two-Guard Walkability of Simple Polygons

WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
Sweeping simple polygons with the minimum number of chain guards

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The two-guard problem revisited and its generalization

ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation

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Abstract

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. Two guards move on the polygon boundary and are required to always be mutually visible. The objective of this study 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 for optimizing this metric, where n is the number of vertices of the given polygon. Our result is obtained by reducing this problem to finding a shortest path between two nodes in a graph of size O(n).