Algebraic gossip on Arbitrary Networks

Consider a network of nodes where each node has a message to communicate to all other nodes. For this communication problem, we analyze a gossip based protocol where coded messages are exchanged. This problem was studied in (4) where a bound to the dissemination time based on the spectral properties of the underlying communication graph is provided. Our contribution is a uniform bound that holds for arbitrary networks. I. I NTRODUCTION There are n nodes in a network, each having an information. The goal is to disseminate the information at every node to every other node in the network. We assume that the network is composed of noiseless links and that the nodes are restricted to communicating with their neighbours defined by the network. Our goal is to characterize the dissemination time for protocols based on pairwise communication between nodes. The problem formulation is motivated by potential appli- cations in sensor networks and databases and is not new. Deb et. al (3) considered the problem where k messages are disseminated in a network of N nodes. However, their analysis is restricted to complete graphs. The problem when all the nodes have information to communicate has been considered by Aoyama and Shah (4) for arbitrary networks. They refer to this problem as the information dissemination problem and report bounds to the dissemination time based on the spectral properties of the underlying graph. We study the same problem and report uniform bounds to the dissemination time, which depend only on the number of nodes and not on the topology of the network. (See discussion in Section. IV for a comparison of results) The paper is organized as follows - The Section. II goes through notation and preliminaries, Section. III provides the main result and Section. IV puts the result in the context of existing results on the problem.