Searching for a mobile intruder in a polygonal region
SIAM Journal on Computing
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Visibility-based pursuit-evasion in a polygonal room with a door
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
An algorithm for searching a polygonal region with a flashlight
Proceedings of the sixteenth annual symposium on Computational geometry
An Efficient Solution to the Corridor Search Problem
JCDCG '98 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
Searching a Simple Polygon by a k-Searcher
ISAAC '00 Proceedings of the 11th International Conference on Algorithms and Computation
The Two-Guard Polygon Walk Problem
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
A linear-time algorithm for finding all door locations that make a room searchable
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
An optimal algorithm for the 1-searchability of polygonal rooms
JCDCG'04 Proceedings of the 2004 Japanese conference on Discrete and Computational Geometry
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We study the problem of searching for a mobile intruder in a polygonal room P with a door d by a mobile searcher. The objective is to decide whether there exists a search schedule to detect the intruder without allowing him to evict 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 k rays emanating from his flashlights. The intruder is detected if he is ever illuminated by a flashlight. For a 1searcher, we present an optimal O(n log n + 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 (驴 n2) is the minimum number of search instructions required to clear P. This improves upon the previous O(n2) time and space bounds. The optimality of our algorithm is obtained by identifying critical visibility events occurred in P and decomposing the search schedule based on them. Furthermore, our method can easily be extended to solve the problem of searching a room by a 2-searcher. The extension is based on a generalization of the notion of visibility to that of link2-visibility.