Searching for a mobile intruder in a polygonal region
SIAM Journal on Computing
Sweeping simple polygons with a chain of guards
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
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
Information Processing Letters
A unified and efficient solution to the room search problem
Computational Geometry: Theory and Applications
An efficient algorithm for the three-guard problem
Discrete Applied Mathematics
Optimum sweeps of simple polygons with two guards
FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
Minimization of the maximum distance between the two guards patrolling a polygonal region
FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
Optimum sweeps of simple polygons with two guards
Information Processing Letters
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Given a simple polygon P with two vertices u and v, the two-guard problem asks if two guards can move on the boundary chains of P from u to v, one clockwise and one counterclockwise, such that they are mutually visible By a close study of the structure of the restrictions placed on the motion of two guards, we present a simpler solution to the two-guard problem The main goal of this paper is to extend the solution for the two-guard problem to that for the three-guard problem, in which the first and third guards move on the boundary chains of P from u to v and the second guard is always kept to be visible from them inside P By introducing the concept of link-2-ray shots, we show a one-to-one correspondence between the structure of the restrictions placed on the motion of two guards and the one placed on the motion of three guards We can decide if there exists a solution for the three-guard problem in O(n log n) time, and if so generate a walk in O(n log n + m) time, where n denotes the number of vertices of P and m (≤ n2) the size of the optimal walk.