Visibility and intersection problems in plane geometry
Discrete & Computational Geometry
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
Introduction to algorithms
Optimal Algorithms for Two-Guard Walkability of Simple Polygons
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
Visibility Algorithms in the Plane
Visibility Algorithms in the Plane
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
Geodesic Fréchet distance inside a simple polygon
ACM Transactions on Algorithms (TALG)
Optimum sweeps of simple polygons with two guards
FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
The two-guard problem revisited and its generalization
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Watchman routes for lines and line segments
Computational Geometry: Theory and Applications
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The two-guard problem asks whether two guards can walk to detect an unpredictable, moving target in a polygonal region P , no matter how fast the target moves, and if so, construct a walk schedule of the guards. For safety, two guards are required to always be mutually visible, and thus, they move on the polygon boundary. Specially, a straight walk requires both guards to monotonically move on the boundary of P from beginning to end, one clockwise and the other counterclockwise. The objective of this paper is to find an optimum straight walk such that the maximum distance between the two guards is minimized. We present an O (n 2 logn ) time algorithm for optimizing this metric, where n is the number of vertices of the polygon P . Our result is obtained by investigating a number of new properties of the min-max walks and converting the problem of finding an optimum walk in the min-max metric into that of finding a shortest path between two nodes in a graph. This answers an open question posed by Icking and Klein.