Taking Advantage of Symmetries: Gathering of Asynchronous Oblivious Robots on a Ring

  • Authors:

  • Ralf Klasing;Adrian Kosowski;Alfredo Navarra

  • Affiliations:

  • LaBRI - Université Bordeaux 1 - CNRS, 351 cours de la Liberation, Talence cedex, France 33405;LaBRI - Université Bordeaux 1 - CNRS, 351 cours de la Liberation, Talence cedex, France 33405 and Department of Algorithms and System Modeling, Gdańsk University of Technology, Gdań ...;Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Perugia, Italy 06123

  • Venue:
  • OPODIS '08 Proceedings of the 12th International Conference on Principles of Distributed Systems
  • Year:
  • 2008

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Abstract

One of the recently considered models of robot-based computing makes use of identical, memoryless mobile units placed in nodes of an anonymous graph. The robots operate in Look-Compute-Move cycles; in one cycle, a robot takes a snapshot of the current configuration (Look), takes a decision whether to stay idle or to move to one of the nodes adjacent to its current position (Compute), and in the latter case makes an instantaneous move to this neighbor (Move). Cycles are performed asynchronously for each robot. In such a restricted scenario, we study the influence of symmetries of the robot configuration on the feasibility of certain computational tasks. More precisely, we deal with the problem of gathering all robots at one node of the graph, and propose a solution based on a symmetry-preserving strategy. When the considered graph is an undirected ring and the number of robots is sufficiently large (more than 18), such an approach is proved to solve the problem for all starting situations, as long as gathering is feasible. In this way we also close the open problem of characterizing symmetric situations on the ring which admit a gathering [R. Klasing, E. Markou, A. Pelc: Gathering asynchronous oblivious mobile robots in a ring, Theor. Comp. Sci. 390(1), 27-39, 2008]. The proposed symmetry-preserving approach, which is complementary to symmetry-breaking techniques found in related work, appears to be new and may have further applications in robot-based computing.