The vertex separation and search number of a graph
Information and Computation
The complexity of pursuit on a graph
Theoretical Computer Science
A game of cops and robbers played on products of graphs
Discrete Mathematics
Gibbs measures and dismantlable graphs
Journal of Combinatorial Theory Series B
An Efficient Communication Strategy for Ad-hoc Mobile Networks
DISC '01 Proceedings of the 15th International Conference on Distributed Computing
Randomized Pursuit-Evasion in Graphs
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Randomized Pursuit-Evasion with Local Visibility
SIAM Journal on Discrete Mathematics
Differential games in large-scale sensor-actuator networks
Proceedings of the 5th international conference on Information processing in sensor networks
Random walks, universal traversal sequences, and the complexity of maze problems
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
Search and pursuit-evasion in mobile robotics
Autonomous Robots
Capturing an evader in polygonal environments with obstacles: The full visibility case
International Journal of Robotics Research
On Confinement of the Initial Location of an Intruder in a Multi-robot Pursuit Game
Journal of Intelligent and Robotic Systems
k-Capture in multiagent pursuit evasion, or the lion and the hyenas
Theoretical Computer Science
| Hi-index | 5.23 |
We investigate the role of the information available to the players on the outcome of the cops and robbers game. This game takes place on a graph and players move along the edges in turns. The cops win the game if they can move onto the robber's vertex. In the standard formulation, it is assumed that the players can ''see'' each other at all times. A graph G is called cop-win if a single cop can capture the robber on G. We study the effect of reducing the cop's visibility. On the positive side, with a simple argument, we show that a cop with small or no visibility can capture the robber on any cop-win graph (even if the robber still has global visibility). On the negative side, we show that the reduction in cop's visibility can result in an exponential increase in the capture time. Finally, we start the investigation of the variant where the visibility powers of the two players are symmetrical. We show that the cop can establish eye contact with the robber on any graph and present a sufficient condition for capture. In establishing this condition, we present a characterization of graphs on which a natural greedy pursuit strategy suffices for capturing the robber.