Distributed Anonymous Mobile Robots: Formation of Geometric Patterns
SIAM Journal on Computing
Distributed Algorithms
Information and Computation
Robots and demons: the code of the origins
FUN'07 Proceedings of the 4th international conference on Fun with algorithms
Fault-tolerant and self-stabilizing mobile robots gathering
DISC'06 Proceedings of the 20th international conference on Distributed Computing
Connectivity-preserving scattering of mobile robots with limited visibility
SSS'10 Proceedings of the 12th international conference on Stabilization, safety, and security of distributed systems
Self-stabilizing gathering with strong multiplicity detection
Theoretical Computer Science
On the self-stabilization of mobile oblivious robots in uniform rings
SSS'12 Proceedings of the 14th international conference on Stabilization, Safety, and Security of Distributed Systems
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In this paper, we look at the time complexity of two agreement problems in networks of oblivious mobile robots, namely, at the gathering and scattering problems. Given a set of robots with arbitrary initial locations and no initial agreement on a global coordinate system, gathering requires that all robots reach the exact same but not predetermined location. In contrast, scattering requires that no two robots share the same location. These two abstractions are fundamental coordination problems in cooperative mobile robotics. Oblivious solutions are appealing for self-stabilization since they are self-stabilizing at no extra cost. As neither gathering nor scattering can be solved deterministically under arbitrary schedulers, probabilistic solutions have been proposed recently. The contribution of this paper is twofold. First, we propose a detailed time complexity analysis of a modified probabilistic gathering algorithm. Using Markov chains tools and additional assumptions on the environment, we prove that the convergence time of gathering can be reduced from O(n^2) (the best known bound) to O(1) or O(logn@?log(logn)), depending on the model of multiplicity detection. Second, using the same technique, we prove that scattering can also be achieved in fault-free systems with the same bounds.