Visibility and intersection problems in plane geometry
Discrete & Computational Geometry
Searching for a mobile intruder in a polygonal region
SIAM Journal on Computing
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Sweeping simple polygons with a chain of guards
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Characterizing LR-visibility polygons and related problems
Computational Geometry: Theory and Applications
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
The two-guard problem revisited and its generalization
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
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
Characterizing and recognizing LR-visibility polygons
Discrete Applied Mathematics
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Given a simple polygon P with two vertices u and v, the three-guard problem asks whether three guards can move from u to v such that the first and third guards are separately on two boundary chains of P from u to v and the second guard is always kept to be visible from two other guards inside P. It is a generalization of the well-known two-guard problem, in which two guards move on the boundary chains from u to v and are always kept to be mutually visible. In this paper, we introduce the concept of link-2-ray shots, which can be considered as ray shots under the notion of link-2-visibility. Then, 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, and generalize the solution for the two-guard problem to that for the three-guard problem. We can decide whether there exists a solution for the three-guard problem in O(nlogn) time, and if so generate a walk in O(nlogn+m) time, where n denotes the number of vertices of P and m(@?n^2) the size of the optimal walk. This improves upon the previous time bounds O(n^2) and O(n^2logn), respectively. Moreover, our results can be used to solve other more sophisticated geometric problems.