Optimization of binary interval consensus

Abstract

Motivated by binary interval consensus algorithm in [1], the bounds for the time of convergence of this type of consensus [4], and using the optimization techniques for doubly stochastic matrices [2, 3], we introduce a distributed way to optimize binary interval consensus. With binary consensus problem, each node initially chooses one of the states 0 or 1 and the goal for the nodes is to agree on the state which was initially held by the majority. Binary interval consensus is a specific type of binary consensus which uses two intermediate states along with 0 and 1 to reduce the probability of error to zero. We show that if the probability of the nodes contacting each other is defined by a doubly stochastic matrix, the optimization of binary interval consensus can be done by reducing the second largest eigenvalue of the rate matrix Q. © 2013 Springer-Verlag London.