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Please use this identifier to cite or link to this item: http://hdl.handle.net/10119/9046

Title: The cost of probabilistic agreement in oblivious robot networks
Authors: Clement, Julien
Defago, Xavier
Potop-Butucaru, Maria Gradinariu
Izumi, Taisuke
Messika, Stephane
Keywords: Distributed systems
Analysis of algorithms
Randomized algorithms
Multi-agent systems
Cooperative robotics
Issue Date: 2010-05-16
Publisher: Elsevier
Magazine name: Information Processing Letters
Volume: 110
Number: 11
Start page: 431
End page: 438
DOI: 10.1016/j.ipl.2010.04.006
Abstract: 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.
Rights: NOTICE: This is the author’s version of a work accepted for publication by Elsevier. Changes resulting from the publishing process, including peer review, editing, corrections, structural formatting and other quality control mechanisms, may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Julien Clement, Xavier Defago, Maria Gradinariu Potop-Butucaru, Taisuke Izumi, and Stephane Messika, Information Processing Letters, 110(11), 2010, 431-438, http://dx.doi.org/10.1016/j.ipl.2010.04.006
URI: http://hdl.handle.net/10119/9046
Material Type: author
Appears in Collections:b10-1. 雑誌掲載論文 (Journal Articles)

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