Fast Distributed Consensus Through Path Averaging on Random Walks

Abstract

Distributed computation of average consensus is an important function in numerous wireless sensor networks and ad-hoc networks applications. In light of the severe resource constraints characterizing these embedded networked systems, it is of paramount importance the design of effective algorithms with low computational, communication, and energy requirements. Randomized gossip are a category of network algorithms that entail communication and information exchange among nodes selected with probabilistic mechanisms. They are considered attractive solutions for solving consensus problems because of their decentralized nature, conceptual simplicity, and capability of adapting to structural network modifications. However, the number of iterations needed by randomized gossip to converge towards consensus is an issue to be addressed to reduce latency and to limit the impact of the algorithm on the lifetime of battery operated devices. Solutions to the problem have been proposed that make use of localization and greedy geographic routing to build overlay graphs on top of a randomized gossip protocol, thus enabling information averaging among non-neighbor nodes and accelerating convergence. The main drawback of this type of approach is that each node is required to know its position, which is not always affordable in terms of costs or not even possible because of the lack of GPS signal. In this article we propose a novel approach to the consensus averaging problem based on a random walk mechanism to identify nodes involved in a computation round, and on a path averaging technique to update more than two nodes into the same round. The resulting algorithm doesn’t rely on any positioning mechanism. Experimental results provide evidence of the improved performance of the proposed method with respect to standard randomized gossip, with considerable gain in terms of convergence speed.