Gathering asynchronous oblivious mobile robots in a ring

  • Authors:

  • Ralf Klasing;Euripides Markou;Andrzej Pelc

  • Affiliations:

  • LaBRI - Université Bordeaux 1 - CNRS, 351 cours de la Libération, 33405 Talence cedex, France;School of Computational Engineering & Science, McMaster University, Hamilton, Ontario L8S4K1, Canada;Département dinformatique, Université du Québec en Outaouais, Gatineau, Québec J8X 3X7, Canada

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2008

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Abstract

We consider the problem of gathering identical, memoryless, mobile robots in one node of an anonymous unoriented ring. Robots start from different nodes of the ring. They operate in Look-Compute-Move cycles and have to end up in the same node. In one cycle, a robot takes a snapshot of the current configuration (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 robot. For an odd number of robots we prove that gathering is feasible if and only if the initial configuration is not periodic, and we provide a gathering algorithm for any such configuration. For an even number of robots we decide the feasibility of gathering except for one type of symmetric initial configurations, and provide gathering algorithms for initial configurations proved to be gatherable.