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Optimal deterministic self-stabilizing vertex coloring in unidirectional anonymous networks

Samuel Bernard 1 Stéphane Devismes 2 Maria Gradinariu Potop-Butucaru 3 Sébastien Tixeuil 1
1 NPA - Networks and Performance Analysis
LIP6 - Laboratoire d'Informatique de Paris 6
3 Regal - Large-Scale Distributed Systems and Applications
LIP6 - Laboratoire d'Informatique de Paris 6, Inria Paris-Rocquencourt
Abstract : A distributed algorithm is self-stabilizing if after faults and attacks hit the system and place it in some arbitrary global state, the systems recovers from this catastrophic situation without external intervention in finite time. Uni-directional networks preclude many common techniques in self-stabilization from being used, such as preserving local predicates. In this paper, we investigate the intrinsic complexity of achieving self-stabilization in unidirectional anonymous general networks, and focus on the classical vertex coloring problem. Specifically, we prove a lower bound of n states per process (where n is the network size) and a recovery time of at least n(n-1)/2 actions in total. We also provide a deterministic algorithm with matching upper bounds that performs in arbitrary unidirectional anonymous graphs.
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Submitted on : Wednesday, April 6, 2016 - 4:25:38 PM
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Samuel Bernard, Stéphane Devismes, Maria Gradinariu Potop-Butucaru, Sébastien Tixeuil. Optimal deterministic self-stabilizing vertex coloring in unidirectional anonymous networks. IPDPS, May 2009, Rome, Italy. pp.1-8, ⟨10.1109/IPDPS.2009.5161053⟩. ⟨hal-01298811⟩



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