Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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)
Chevaleyre, Y.: Theoretical analysis of the multi-agent patrolling problem. In: Proc. IEEE/WIC/ACM Int. Conf. Intelligent Agent Technology, pp. 302–308 (2004)
Clark, J., Fierro, R.: Mobile robotic sensors for perimeter detection and tracking. ISA Transactions 46, 3–13 (2007)
Czyzowicz, J., Gąsieniec, L., Kosowski, A., Kranakis, E.: Boundary Patrolling by Mobile Agents with Distinct Maximal Speeds. In: Demetrescu, C., Halldórsson, M.M. (eds.) ESA 2011. LNCS, vol. 6942, pp. 701–712. Springer, Heidelberg (2011)
Elmaliach, Y., Agmon, N., Kaminka, G.A.: Multi-robot area patrol under frequency constraints. Ann. Math. Artif. Intell. 57, 293–320 (2009)
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)
Pasqualetti, F., Franchi, A., Bullo, F.: On optimal cooperative patrolling. In: Proc. 49th IEEE Conference on Decision and Control, pp. 7153–7158 (2010)
Yanovski, V., Wagner, I.A., Bruckstein, A.M.: A distributed ant algorithm for efficiently patrolling a network. Algorithmica 37, 165–186 (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kawamura, A., Kobayashi, Y. (2012). Fence Patrolling by Mobile Agents with Distinct Speeds. In: Chao, KM., Hsu, Ts., Lee, DT. (eds) Algorithms and Computation. ISAAC 2012. Lecture Notes in Computer Science, vol 7676. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35261-4_62
Download citation
DOI: https://doi.org/10.1007/978-3-642-35261-4_62
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35260-7
Online ISBN: 978-3-642-35261-4
eBook Packages: Computer ScienceComputer Science (R0)