Visibility and intersection problems in plane geometry
Discrete & Computational Geometry
Searching for a mobile intruder in a polygonal region
SIAM Journal on Computing
Computational Geometry: Theory and Applications - Special issue: computational geometry, theory and applications
Visibility-based pursuit-evasion in a polygonal room with a door
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
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
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
An efficient algorithm for the three-guard problem
Discrete Applied Mathematics
Searching a Circular Corridor with Two Flashlights
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Simple characterization of LR-visibility polygons
CGGA'10 Proceedings of the 9th international conference on Computational Geometry, Graphs and Applications
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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We study the problem of searching for a mobile intruder in a polygonal region P with a door d (called a room) by a mobile searcher. The objective is to decide whether there exists a search schedule for the searcher to detect the intruder without allowing him to exit P through d, no matter how fast he moves, and if so, generate a search schedule. A searcher is called the k-searcher if he holds k flashlights and can see only along the rays of the flashlights emanating from his position, or two guards if two endpoints of the 1-searcher's flashlight move on the polygon boundary continuously. In this paper, we develop a simple, unified solution to the room search problem. The characterizations of the k-searchable and two-guard walkable rooms are all given in terms of components and deadlocks. A study on the structure of non-redundant components and deadlocks gives critical visibility events which occur in any search schedule, and a vertex of P at which our search schedule ends. Our characterizations are not only simple but also lead to efficient algorithms for all decision problems and schedule reporting problems. Particularly, we present optimal O(n) time algorithms for determining the 1-searchability and the two-guard walkability of a room, and an O(nlogn+m) time and O(n) space algorithm for generating a search schedule, if it exists, where n is the number of vertices of P and m(=