Triangulating a simple polygon in linear time
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
Characterizing LR-visibility polygons and related problems
Computational Geometry: Theory and Applications
Simple algorithms for searching a polygon with flashlights
Information Processing Letters
Optimal Algorithms for Two-Guard Walkability of Simple Polygons
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
Efficient Algorithms for Searching a Polygonal Room with a Door
JCDCG '00 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
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
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The 1-searcher is a mobile guard who can see only along a ray emanating from his position and can continuously change the direction of the ray with bounded speed. A polygonal region P with a specified point d on its boundary is called a room, and denoted by (P, d). The room (P, d) is said to be 1-searchable if the searcher, starting at the point d, can eventually see a mobile intruder who moves arbitrarily fast inside P, without allowing the intruder to touch d. We present an optimal O(n) time algorithm to determine whether there is a point x on the boundary of P such that the room (P, x) is 1-searchable. This improves upon the previous O(n log n) time bound, which was established for determining whether or not a room (P, d) is 1-searchable, where d is a given point on the boundary of P.