Gossip-based Computation of Average: a Closest Point Search Approach

Due to simplicity and robustness, gossip based algorithms for data aggregation have recently received significant attention for applications in ad hoc and wireless sensor networks. Nodes in such networks operate under limited communication, computation, and energy resources. However, a common drawback of many gossip based protocols is the waste of energy in passing around redundant information multiple times. Thus gossip algorithms need to be re-designed in order to be applicable for energy constraint networks. In this paper, we study the averaging problem under the gossip constraint. In a network of n nodes, each node u_i holds a value x_i at the beginning and the objective is to compute the global average of these values in a distributed manner, while consuming least amount of energy. By formulating the problem as a closest point search in a n- dimensional cube, we demonstrate that the true average can be computed in the optimal O(log n) rounds without any probability involved. Moreover, the proposed algorithm is shown to outperform existing approaches for wireless sensor network in terms of the number of radio transmissions.