Shortest watchman routes in simple polygons
Discrete & Computational Geometry
Searching for a mobile intruder in a polygonal region
SIAM Journal on Computing
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Bushiness and a tight worst-case upper bound on the search number of a simple polygon
Information Processing Letters
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
Efficient Algorithms for Searching a Polygonal Room with a Door
JCDCG '00 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
The Two-Guard Polygon Walk Problem
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
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The polygon search problem is the problem of searching for a mobile intruder in a simple polygon by the mobile searcher who holds flashlights and whose visibility is limited to the rays emanating from his flashlights. The goal is to decide whether there exists a search schedule for the searcher to detect the intruder, no matter how fast he moves, and if so, generate such a schedule. A searcher is called the k-searcher if he can see along k rays emanating from his position, and the ∞-searcher if he has a 360° field of vision. We present necessary and sufficient conditions for a polygon to be searchable by a k-searcher (for k = 1 or 2), and give O(n2) time algorithms for testing the k-searchability of simple polygons and generating a search schedule if it exists. We also show that any polygon that is searchable by an ∞-searcher is searchable by a 2-searcher. Our results solve a long-standing open problem in computational geometry and robotics, and confirm a conjecture due to Suzuki and Yamashita.