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
Sweeping simple polygons with the minimum number of chain guards
Information Processing Letters
A unified and efficient solution to the room search problem
Computational Geometry: Theory and Applications
The Two-Guard Polygon Walk Problem
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Surveillance of a polygonal area by a mobile searcher from the boundary: searchability testing
ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
Searching a polygonal region by two guards
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
Optimum sweeps of simple polygons with two guards
FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
Hide-and-seek: algorithms for polygonWalk problems
TAMC'11 Proceedings of the 8th annual 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
Finding the minimum-distance schedule for a boundary searcher with a flashlight
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
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We consider the problem of searching for a moving target with unbounded speed in a dark polygonal region by a searcher. The searcher continuously moves on the polygon boundary and can see only along the rays of the flashlights emanating from his position at a time. We present necessary and sufficient conditions for a polygon of n vertices to be searchable from the boundary. Our two main results are the following: We present an O(n log n) time and O(n) space algorithm for testing the searchability of simple polygons. Moreover, a search schedule can be reported in time linear in its size I, if it exists. For the searcher having full 360° vision, I n, and for the searcher having only one flashlight, I n2. Our result improves upon the previous O(n2) time and space solution, given by LaValle et al [5]. Also, the linear bound for the searcher having full 360° vision solves an open problem posed by Suzuki et al [7]. We show the equivalence of the abilities of the searcher having only one flashlight and the one having full 360° vision. Although the same result has been obtained by Suzuki et al [7], their proof is long and complicated, due to lack of the characterization of boundary search.