Abstract
We consider the problem of gathering identical, memoryless, mobile agents in one node of an anonymous graph. Agents start from different nodes of the graph. They operate in Look-Compute-Move cycles and have to end up in the same node. In one cycle, an agent takes a snapshot of its immediate neighborhood (Look), makes a decision to stay idle or to move to one of its adjacent nodes (Compute), and in the latter case makes an instantaneous move to this neighbor (Move). Cycles are performed asynchronously for each agent. The novelty of our model with respect to the existing literature on gathering asynchronous oblivious agents in graphs is that the agents have very restricted perception capabilities: they can only see their immediate neighborhood.
An initial configuration of agents is called gatherable if there exists an algorithm that gathers all the agents of the configuration in one node and keeps them idle from then on, regardless of the actions of the asynchronous adversary. (The algorithm can be even tailored to gather this specific configuration.) The gathering problem is to determine which configurations are gatherable and find a (universal) algorithm which gathers all gatherable configurations. We give a complete solution of the gathering problem for regular bipartite graphs. Our main contribution is the proof that the class of gatherable initial configurations is very small: it consists only of “stars” (an agent A with all other agents adjacent to it) of size at least 3. On the positive side we give an algorithm accomplishing gathering for every gatherable configuration.
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References
Agmon, N., Peleg, D.: Fault-Tolerant Gathering Algorithms for Autonomous Mobile Robots. SIAM J. Comput. 36(1), 56–82 (2006)
Alpern, S., Gal, S.: The Theory of Search Games and Rendezvous. Kluwer Academic Publishers, Dordrecht (2002)
Ando, H., Oasa, Y., Suzuki, I., Yamashita, M.: Distributed Memoryless Point Convergence Algorithm for Mobile Robots with Limited Visibility. IEEE Trans. on Robotics and Automation 15(5), 818–828 (1999)
Cieliebak, M.: Gathering Non-oblivious Mobile Robots. In: Farach-Colton, M. (ed.) LATIN 2004. LNCS, vol. 2976, pp. 577–588. Springer, Heidelberg (2004)
Cieliebak, M., Flocchini, P., Prencipe, G., Santoro, N.: Solving the Robots Gathering Problem. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 1181–1196. Springer, Heidelberg (2003)
Cohen, R., Peleg, D.: Robot Convergence via Center-of-Gravity Algorithms. In: Kralovic, R., Sýkora, O. (eds.) SIROCCO 2004. LNCS, vol. 3104, pp. 79–88. Springer, Heidelberg (2004)
Czyzowicz, J., Labourel, A., Pelc, A.: How to meet asynchronously (almost) everywhere. In: Proc. 21st Annual ACM-SIAM Symposium on Discrete Algorithms (SODA ), pp. 22–30 (2010)
De Marco, G., Gargano, L., Kranakis, E., Krizanc, D., Pelc, A., Vaccaro, U.: Asynchronous deterministic rendezvous in graphs. Theoretical Computer Science 355, 315–326 (2006)
Dessmark, A., Fraigniaud, P., Kowalski, D., Pelc, A.: Deterministic rendezvous in graphs. Algorithmica 46, 69–96 (2006)
Flocchini, P., Kranakis, E., Krizanc, D., Santoro, N., Sawchuk, C.: Multiple Mobile Agent Rendezvous in a Ring. In: Farach-Colton, M. (ed.) LATIN 2004. LNCS, vol. 2976, pp. 599–608. Springer, Heidelberg (2004)
Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Gathering of Asynchronous Robots with Limited Visibility. Theoretical Computer Science 337(1-3), 147–168 (2005)
Izumi, T., Izumi, T., Kamei, S., Ooshita, F.: Mobile robots gathering algorithm with local weak multiplicity in rings. In: Patt-Shamir, B., Ekim, T. (eds.) SIROCCO 2010. LNCS, vol. 6058, pp. 101–113. Springer, Heidelberg (2010)
Klasing, R., Kosowski, A., Navarra, A.: Taking advantage of symmetries: gathering of asynchronous oblivious robots on a ring. In: Baker, T.P., Bui, A., Tixeuil, S. (eds.) OPODIS 2008. LNCS, vol. 5401, pp. 446–462. Springer, Heidelberg (2008)
Klasing, R., Markou, E., Pelc, A.: Gathering asynchronous oblivious mobile robots in a ring. Theoretical Computer Science 390, 27–39 (2008)
Kowalski, D., Pelc, A.: Polynomial deterministic rendezvous in arbitrary graphs. In: Fleischer, R., Trippen, G. (eds.) ISAAC 2004. LNCS, vol. 3341, pp. 644–656. Springer, Heidelberg (2004)
Prencipe, G.: CORDA: Distributed Coordination of a Set of Autonomous Mobile Robots. In: Proc. ERSADS, pp. 185–190 (2001)
Prencipe, G.: Impossibility of gathering by a set of autonomous mobile robots. Theoretical Computer Science 384, 222–231 (2007)
Suzuki, I., Yamashita, M.: Distributed Anonymous Mobile Robots: Formation of Geometric Patterns. SIAM J. Comput. 28(4), 1347–1363 (1999)
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Guilbault, S., Pelc, A. (2011). Gathering Asynchronous Oblivious Agents with Local Vision in Regular Bipartite Graphs. In: Kosowski, A., Yamashita, M. (eds) Structural Information and Communication Complexity. SIROCCO 2011. Lecture Notes in Computer Science, vol 6796. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22212-2_15
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DOI: https://doi.org/10.1007/978-3-642-22212-2_15
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