Stabilizing Maximal Independent Set in Unidirectional Networks is Hard

Toshimitsu Masuzawa 1 Sébastien Tixeuil 2, 3
2 GRAND-LARGE - Global parallel and distributed computing
LRI - Laboratoire de Recherche en Informatique, LIFL - Laboratoire d'Informatique Fondamentale de Lille, UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France, CNRS - Centre National de la Recherche Scientifique : UMR8623
Abstract : A distributed algorithm is self-stabilizing if after faults and attacks hit the system and place it in some arbitrary global state, the system recovers from this catastrophic situation without external intervention in finite time. In this paper, we consider the problem of constructing self-stabilizingly a \emph{maximal independent set} in uniform unidirectional networks of arbitrary shape. On the negative side, we present evidence that in uniform networks, \emph{deterministic} self-stabilization of this problem is \emph{impossible}. Also, the \emph{silence} property (\emph{i.e.} having communication fixed from some point in every execution) is impossible to guarantee, either for deterministic or for probabilistic variants of protocols. On the positive side, we present a deterministic protocol for networks with arbitrary unidirectional networks with unique identifiers that exhibits polynomial space and time complexity in asynchronous scheduling. We complement the study with probabilistic protocols for the uniform case: the first probabilistic protocol requires infinite memory but copes with asynchronous scheduling, while the second probabilistic protocol has polynomial space complexity but can only handle synchronous scheduling. Both probabilistic solutions have expected polynomial time complexity.
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https://hal.inria.fr/inria-00368950
Contributor : Sébastien Tixeuil <>
Submitted on : Wednesday, March 18, 2009 - 9:29:20 AM
Last modification on : Thursday, March 21, 2019 - 1:07:49 PM
Long-term archiving on : Tuesday, June 8, 2010 - 11:35:58 PM

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  • HAL Id : inria-00368950, version 1
  • ARXIV : 0903.3106

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Toshimitsu Masuzawa, Sébastien Tixeuil. Stabilizing Maximal Independent Set in Unidirectional Networks is Hard. [Research Report] RR-6880, INRIA. 2009, pp.21. ⟨inria-00368950⟩

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