Fence Patrolling by Mobile Agents with Distinct Speeds
Suppose we want to patrol a fence (line segment) using k mobile agents with speeds v 1, …, v k so that every point on the fence is visited by an agent at least once in every unit time period. Czyzowicz et al. conjectured that the maximum length of the fence that can be patrolled is (v 1 + … + v k ) / 2, which is achieved by the simple strategy where each agent i moves back and forth in a segment of length v i / 2. We disprove this conjecture by a counterexample involving k = 6 agents. We also show that the conjecture is true for k ≤ 3.
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- 1.Almeida, A., Ramalho, G., Santana, H., Tedesco, P., Menezes, T., Corruble, V., Chevaleyre, Y.: Recent advances on multi-agent patrolling. In: Proc. 17th Brazilian Symposium on Artificial Intelligence, pp. 474–483 (2004)Google Scholar
- 2.Chevaleyre, Y.: Theoretical analysis of the multi-agent patrolling problem. In: Proc. IEEE/WIC/ACM Int. Conf. Intelligent Agent Technology, pp. 302–308 (2004)Google Scholar
- 6.Elmaliach, Y., Shiloni, A., Kaminka, G.A.: A realistic model of frequency-based multi-robot polyline patrolling. In: Proc. 7th Int. Conf. Autonomous Agents and Multiagent Systems, pp. 63–70 (2008)Google Scholar
- 7.Pasqualetti, F., Franchi, A., Bullo, F.: On optimal cooperative patrolling. In: Proc. 49th IEEE Conference on Decision and Control, pp. 7153–7158 (2010)Google Scholar