Randomized Consensus with Attractive and Repulsive Links

Guodong Shi 1 Alexandre Proutière 1, 2 Mikael Johansson 1 Karl H. Johansson 1
2 DYOGENE - Dynamics of Geometric Networks
DI-ENS - Département d'informatique de l'École normale supérieure, Inria Paris-Rocquencourt, CNRS - Centre National de la Recherche Scientifique : UMR8548
Abstract : We study convergence properties of a randomized consensus algorithm over a graph with both attractive and repulsive links. At each time instant, a node is randomly selected to interact with a random neighbor. Depending on if the link between the two nodes belongs to a given subgraph of attractive or repulsive links, the node update follows a standard attractive weighted average or a repulsive weighted average, respectively. The repulsive update has the opposite sign of the standard consensus update. In this way, it counteracts the consensus formation and can be seen as a model of link faults or malicious attacks in a communication network, or the impact of trust and antagonism in a social network. Various probabilistic convergence and divergence conditions are established. A threshold condition for the strength of the repulsive action is given for convergence in expectation: when the repulsive weight crosses this threshold value, the algorithm transits from convergence to divergence. An explicit value of the threshold is derived for classes of attractive and repulsive graphs. The results show that a single repulsive link can sometimes drastically change the behavior of the consensus algorithm. They also explicitly show how the robustness of the consensus algorithm depends on the size and other properties of the graphs.
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https://hal.archives-ouvertes.fr/hal-00920074
Contributor : Alexandre Proutiere <>
Submitted on : Tuesday, December 17, 2013 - 4:41:54 PM
Last modification on : Tuesday, January 29, 2019 - 3:10:35 PM

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  • HAL Id : hal-00920074, version 1
  • ARXIV : 1309.2574

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Guodong Shi, Alexandre Proutière, Mikael Johansson, Karl H. Johansson. Randomized Consensus with Attractive and Repulsive Links. CDC 2013 - 52nd IEEE Conference on Decision and Control, Dec 2013, Florence, Italy. 8 p. ⟨hal-00920074⟩

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