Abstract
The gathering problem has been largely studied in the last years with respect to various basic graph topologies. The requirement is to move a team of robots initially placed at different vertices of the input graph towards a common vertex, and to let them remain at such a vertex. Robots move based on the so called Look-Compute-Move model. Each time a robot wakes-up, it perceives the current configuration in terms of occupied vertices (Look), it decides whether to move towards one of its neighbors (Compute), and in the positive case it makes the computed move instantaneously (Move). All the phases are performed asynchronously for each robot. So far, the goal has been mainly to detect the minimal assumptions that allow to accomplish the gathering task, without taking care of any cost measure of the provided solutions. In this paper, we are interested in devising optimal algorithms in terms of total number of moves the robots have to perform in order to finalize the gathering. In particular, we consider infinite grids as input graphs, and we fully characterize when optimal gathering is achievable by providing a distributed algorithm.
Work partially supported by the following Research Grants: 2010N5K7EB “PRIN 2010” ARS TechnoMedia (Algoritmica per le Reti Sociali Tecno-mediate) and 2012C4E3KT “PRIN 2012” Amanda (Algorithmics for MAssive and Networked DAta), both from the Italian Ministry of University and Research.
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References
D’Angelo, G., Di Stefano, G., Klasing, R., Navarra, A.: Gathering of robots on anonymous grids and trees without multiplicity detection. Theor. Comput. Sci. (to appear)
D’Angelo, G., Di Stefano, G., Navarra, A.: Gathering on rings under the look-compute-move model. Distributed Computing 27(4), 255–285 (2014)
D’Angelo, G., Di Stefano, G., Navarra, A.: Gathering asynchronous and oblivious robots on basic graph topologies under the look-compute-move model. In: Search Theory: A Game Theoretic Perspective, pp. 197–222. Springer (2013)
Degener, B., Kempkes, B., Langner, T., Meyer, F.: A tight runtime bound for synchronous gathering of autonomous robots with limited visibility. In: Proc. of the 23rd ACM Symp. on Parallelism in Algorithms and Architectures (SPAA), pp. 139–148 (2011)
Devismes, S., Lamani, A., Petit, F., Raymond, P., Tixeuil, S.: Optimal grid exploration by asynchronous oblivious robots. In: Richa, A.W., Scheideler, C. (eds.) SSS 2012. LNCS, vol. 7596, pp. 64–76. Springer, Heidelberg (2012)
Di Stefano, G., Navarra, A.: Optimal gathering of oblivious robots in anonymous graphs. In: Moscibroda, T., Rescigno, A.A. (eds.) SIROCCO 2013. LNCS, vol. 8179, pp. 213–224. Springer, Heidelberg (2013)
Dieudonné, Y., Pelc, A., Villain, V.: How to meet asynchronously at polynomial cost. In: Proc. of the 32nd ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing (PODC), pp. 92–99 (2013)
Flocchini, P., Prencipe, G., Santoro, N.: Distributed Computing by Oblivious Mobile Robots. Synthesis Lectures on Distributed Computing Theory. Morgan & Claypool (2012)
Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Gathering of asynchronous robots with limited visibility. Theor. Comput. Sci. 337, 147–168 (2005)
Izumi, T., Izumi, T., Kamei, S., Ooshita, F.: Randomized gathering of mobile robots with local-multiplicity detection. In: Guerraoui, R., Petit, F. (eds.) SSS 2009. LNCS, vol. 5873, pp. 384–398. Springer, Heidelberg (2009)
Klasing, R., Kosowski, A., Navarra, A.: Taking advantage of symmetries: Gathering of many asynchronous oblivious robots on a ring. Theor. Comput. Sci. 411, 3235–3246 (2010)
Klasing, R., Markou, E., Pelc, A.: Gathering asynchronous oblivious mobile robots in a ring. Theor. Comput. Sci. 390, 27–39 (2008)
Kupitz, Y., Martini, H.: Geometric aspects of the generalized Fermat-Torricelli problem. Intuitive Geometry, vol. 6. Bolyai Society Math Studies (1997)
Suzuki, I., Yamashita, M.: Distributed anonymous mobile robots: Formation of geometric patterns. SIAM J. Comput. 28(4), 1347–1363 (1999)
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Di Stefano, G., Navarra, A. (2014). Optimal Gathering on Infinite Grids. In: Felber, P., Garg, V. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2014. Lecture Notes in Computer Science, vol 8756. Springer, Cham. https://doi.org/10.1007/978-3-319-11764-5_15
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DOI: https://doi.org/10.1007/978-3-319-11764-5_15
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