Constrained Delaunay triangulations
SCG '87 Proceedings of the third annual symposium on Computational geometry
Searching for a mobile intruder in a polygonal region
SIAM Journal on Computing
Sweeping simple polygons with a chain of guards
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Solution of David Gale's lion and man problem
Theoretical Computer Science
Visibility-Based Pursuit-Evasion in a Polygonal Region by a Searcher
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Randomized Pursuit-Evasion in Graphs
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Visibility-based Pursuit-evasion with Limited Field of View
International Journal of Robotics Research
An annotated bibliography on guaranteed graph searching
Theoretical Computer Science
A framework for pursuit evasion games in Rn
Information Processing Letters
Lion and man game in the presence of a circular obstacle
IROS'09 Proceedings of the 2009 IEEE/RSJ international conference on Intelligent robots and systems
Search and pursuit-evasion in mobile robotics
Autonomous Robots
Randomized pursuit-evasion in a polygonal environment
IEEE Transactions on Robotics
On Discrete-Time Pursuit-Evasion Games With Sensing Limitations
IEEE Transactions on Robotics
Capturing an evader in a polygonal environment with obstacles
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Three
Capturing an evader in polygonal environments with obstacles: The full visibility case
International Journal of Robotics Research
Computing highly occluded paths on a terrain
Proceedings of the 21st ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
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We investigate the following problem in the visibility-based discrete-time model of pursuit evasion in the plane: how many pursuers are needed to capture an evader in a polygonal environment with obstacles under the minimalist assumption that pursuers and the evader have the same maximum speed? When the environment is a simply-connected (hole-free) polygon of n vertices, we show that Θ (√n) pursuers are both necessary and sufficient in the worst-case. When the environment is a polygon with holes, we prove a lower bound of Ω (n2/3) and an upper bound of O(n5/6) for the number of pursuers that are needed in the worst-case, where n is the total number of vertices including the hole boundaries. More precisely, if the polygon contains h holes, our upper bound is O(n1/2 h1/4), for h ≤ n2/3, and O(n1/3 h1/2) otherwise. These bounds show that capture with minimal assumptions requires significantly more pursuers than what is possible either for visibility detection where pursuers win if one of them can see the evader [Guibas et al. 1999], or for capture when players' movement speed is small compared to "features" of the environment [Klein and Suri, 2012].