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
Optimal Algorithms for Two-Guard Walkability of Simple Polygons
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
Visibility-Based Pursuit-Evasion in a Polygonal Region by a Searcher
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Sweeping simple polygons with the minimum number of chain guards
Information Processing Letters
The two-guard problem revisited and its generalization
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
A characterization of polygonal regions searchable from the boundary
IJCCGGT'03 Proceedings of the 2003 Indonesia-Japan joint conference on Combinatorial Geometry and Graph Theory
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
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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. For safety, two guards are required to always be mutually visible, and thus, they should move on the polygon boundary. Our objective in this paper 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(n2) time and O(n) space algorithm, where n is the number of vertices of the given polygon. This new result is obtained by converting the problem of sweeping simple polygons with two guards into that of finding a shortest path between two nodes in a graph of size O(n).