Finding the minimum-distance schedule for a boundary searcher with a flashlight

Authors:
Tsunehiko Kameda;Ichiro Suzuki;John Z. Zhang
Affiliations:
School of Computing Science, Simon Fraser University, Canada;Dept. of Computer Science, University of Wisconsin at Milwaukee;Dept. of Mathematics and Computer Science, University of Lethbridge, Canada
Venue:
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Year:
2010

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Abstract

Consider a dark polygonal region in which intruders move freely, trying to avoid detection. A robot, which is equipped with a flashlight, moves along the polygon boundary to illuminate all intruders. We want to minimize the total distance traveled by the robot until all intruders are detected in the worst case. We present an O(nlogn) time and O(n) space algorithm for optimizing this metric, where n is the number of vertices of the given polygon. This improves upon the best known time and space complexities of O(n2) and O(n2), respectively. The distance graph plays a critical role in our analysis and algorithm design.