Quantized Consensus by Means of Gossip Algorithm

• Published in: IEEE transactions on automatic control Vol. 57; no. 1; pp. 19 - 32
• Main Authors: Lavaei, J., Murray, R. M.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.01.2012; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Computer science; control theory; systems; Computer systems and distributed systems. User interface; Convergence; Counters; Distributed computation; Exact sciences and technology; Exchanging; gossip algorithm; Graphs; Heuristic algorithms; Laplace equations; network; Networks; Optimization; Probability distribution; Quantization; Software; Steady-state; Stochasticity; Studies; Upper bound; Lower bound; Averaging method; Probabilistic approach; gossip algorithm; Updating; Distributed system; Topology; Randomized algorithm; Distributed computing; Convex programming; Consensus; Laplacian; network; Upper bound; Signal quantization; Gossiping(all to all); Distributed computation; quantization
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2011.2160593

This paper deals with the distributed averaging problem over a connected network of agents, subject to a quantization constraint. It is assumed that at each time update, only a pair of agents can update their own states in terms of the quantized data being exchanged. The agents are also required to communicate with one another in a stochastic fashion. It is shown that a quantized consensus is reached for an arbitrary quantizer by means of the stochastic gossip algorithm proposed in a recent paper. The expected value of the time at which a quantized consensus is reached is lower and upper bounded in terms of the topology of the graph for a uniform quantizer. In particular, it is shown that these bounds are related to the principal submatrices of the weighted Laplacian matrix. A convex optimization is also proposed to determine a set of probabilities used to pick a pair of agents that leads to a fast convergence of the gossip algorithm.