Distributed Multivalued Consensus

Motivated by the distributed binary consensus algorithm in Perron et al. [(2009) UsingThree States for Binary Consensus on Complete Graphs. INFOCOM 2009, IEEE, April, pp. 2527–2535], we propose a distributed algorithm for the multivalued consensus problem. In the multivalued consensus problem, each node initially chooses from one of k available choices and the objective of all nodes is to find the choice which was initially chosen by the majority in a distributed fashion. Although the voter model (e.g. Hassin,Y. and Peleg, D. (2002) Distributed probabilistic polling and applications to proportionate agreement. Inf. Comput., 171, 248–268) can be used to find a consensus on multiple choices, it only guarantees consensus and not the consensus on the majority. We derive the time of convergence and an upper bound for the probability of error of our proposed algorithm which shows that, similar to Perron et al. [(2009) Using Three States for Binary Consensus on Complete Graphs. INFOCOM 2009, IEEE, pp. 2527–2535], having an additional state would result in significant improvement of both the convergence time and the probability of error for complete graphs. We also show that our algorithm could be used in Erdös–Rényi and regular graphs by simulations.