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
Characterizing LR-visibility polygons and related problems
Computational Geometry: Theory and Applications
Efficient Algorithms for Searching a Polygonal Room with a Door
JCDCG '00 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
Online polygon search by a seven-state boundary 1-searcher
IEEE Transactions on Robotics
The Two-Guard Polygon Walk Problem
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Hide-and-seek: algorithms for polygonWalk problems
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
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A room is a simple polygon with a prespecified point, called the door, on its boundary. Search may be conducted by two guards on the boundary who keep mutual visibility at all times, or by a single boundary searcher with a flashlight. Search starts at the door, and must detect any intruder that was in the room at the time the search started, preventing the intruder from escaping through the door. A room may or may not be searchable, depending on where the door is placed or no matter where the door is placed. We want to find all intervals on the boundary where the door can be placed for the resultant room to be searchable. It is known that this problem can be solved in O(n log n) time, if the given polygon has n sides. We improve this complexity to O(n).