On k-hulls and related problems
SIAM Journal on Computing
Solution of David Gale's lion and man problem
Theoretical Computer Science
The role of information in the cop-robber game
Theoretical Computer Science
A framework for pursuit evasion games in Rn
Information Processing Letters
Randomized pursuit-evasion in a polygonal environment
IEEE Transactions on Robotics
On Discrete-Time Pursuit-Evasion Games With Sensing Limitations
IEEE Transactions on Robotics
Algorithms in Combinatorial Geometry
Algorithms in Combinatorial Geometry
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We consider the following generalization of the classical pursuit-evasion problem, which we call k-capture. A group of n pursuers (hyenas) wish to capture an evader (lion) who is free to move in an m-dimensional Euclidean space, the pursuers and the evader can move with the same maximum speed, and at least k pursuers must simultaneously reach the evader@?s location to capture it. If fewer than k pursuers reach the evader, then those pursuers get destroyed by the evader. Under what conditions can the evader be k-captured? We study this problem in the discrete time, continuous space model and prove that k-capture is possible if and only if there exists a time when the evader lies in the interior of the pursuers@? k-Hull. When the pursuit occurs inside a compact, convex subset of the Euclidean space, we show through an easy constructive strategy that k-capture is always possible.