Theoretical Computer Science
The complexity of searching a graph
Journal of the ACM (JACM)
Searching for a mobile intruder in a polygonal region
SIAM Journal on Computing
Recontamination does not help to search a graph
Journal of the ACM (JACM)
Eavesdropping games: a graph-theoretic approach to privacy in distributed systems
Journal of the ACM (JACM)
Sweeping simple polygons with a chain of guards
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
An efficient communication strategy for ad-hoc mobile networks
Proceedings of the twentieth annual ACM symposium on Principles of distributed computing
A framework for pursuit evasion games in Rn
Information Processing Letters
Visibility-based Pursuit-evasion with Limited Field of View
International Journal of Robotics Research
Escaping offline searchers and isoperimetric theorems
Computational Geometry: Theory and Applications
Efficient Multi-robot Search for a Moving Target
International Journal of Robotics Research
Multi-step multi-sensor hider-seeker games
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
A framework for pursuit evasion games in Rn
Information Processing Letters
Distributed hybrid control for multiple-pursuer multiple-evader games
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
Escaping off-line searchers and a discrete isoperimetric theorem
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Resolving the pursuit evasion problem in known environment using graph theory
International Journal of Bio-Inspired Computation
Vision-Based Pursuit-Evasion in a Grid
SIAM Journal on Discrete Mathematics
Search and pursuit-evasion in mobile robotics
Autonomous Robots
Environment characterization for non-recontaminating frontier-based robotic exploration
PRIMA'11 Proceedings of the 14th international conference on Agents in Principle, Agents in Practice
Model checking knowledge in pursuit evasion games
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
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We analyse a randomized pursuit-evasion game played by two players on a graph, a hunter and a rabbit. Let $G$ be any connected, undirected graph with $n$ nodes. The game is played in rounds and in each round both the hunter and the rabbit are located at a node of the graph. Between rounds both the hunter and the rabbit can stay at the current node or move to another node. The hunter is assumed to be restricted to the graph $G$: in every round, the hunter can move using at most one edge. For the rabbit we investigate two models: in one model the rabbit is restricted to the same graph as the hunter, and in the other model the rabbit is unrestricted, i.e., it can jump to an arbitrary node in every round.We say that the rabbit is caught as soon as hunter and rabbit are located at the same node in a round. The goal of the hunter is to catch the rabbit in as few rounds as possible, whereas the rabbit aims to maximize the number of rounds until it is caught. Given a randomized hunter strategy for $G$, the escape length for that strategy is the worst case expected number of rounds it takes the hunter to catch the rabbit, where the worst case is with regard to all (possibly randomized) rabbit strategies. Our main result is a hunter strategy for general graphs with an escape length of only $\O(n \log (\diam(G)))$ against restricted as well as unrestricted rabbits. This bound is close to optimal since $\Omega(n)$ is a trivial lower bound on the escape length in both models. Furthermore, we prove that our upper bound is optimal up to constant factors against unrestricted rabbits.