Request-based gossiping

Abstract

By the distributed averaging problem is meant the problem of computing the average value of a set of numbers possessed by the agents in a distributed network using only communication between neighboring agents. Gossiping is a well-known approach to the problem which seeks to iteratively arrive at a solution by allowing each agent to interchange information with at most one neighbor at each iterative step. Crafting a gossiping protocol which accomplishes this is challenging because gossiping is an inherently collaborative process which can lead to deadlock unless careful precautions are taken to ensure that it does not. In this paper we present three gossiping protocols. We show by example that the first can deadlock. While the second cannot, it requires a degree of network-wide coordination which may not be possible to secure in some applications. The third protocol uses only local information, is guaranteed to avoid deadlock, and requires fewer transmissions per iteration than standard broadcastbased distributed averaging protocols.

Asynchronous distributed averaging using double linear iterations

“…Prompted by these considerations, we propose a "roundrobin-based" protocol in Section V which is guaranteed to solve the asynchronous distributed averaging problem for directed neighbor graphs under appropriate assumptions. Similar ideas have been proposed in [19], [20] to reduce the total number of transmissions.…”

“…It is worth noting that in the synchronous case, the total number of transmissions per iteration required for all n agents is n. Thus for any fixed N, fewer transmissions are required per iteration to do averaging with the protocol under consideration than are required per iteration to do averaging via broadcast algorithms [10], the modified Metropolis algorithm [20], and the deterministic request-based gossiping protocol [19].…”

Intelligent Distributed Control

“…In [10] we provide a compact proof of the fact [19] that the rate of convergence of periodic multi-gossiping sequences associated with the tree does not depend on the order in which the individual multi-gossips in the sequence take place. We've also sought to understand the subtleties of aperiodic gossiping [14]. In [15] we show that the classical concept of a contraction coefficient which is important in quantifying convergence rates for nonhomogeneous Markov Chains, could be viewed as but one of a number of different types of semi-norms of suitably defined stochastic matrices.…”

“…In [15] we show that the classical concept of a contraction coefficient which is important in quantifying convergence rates for nonhomogeneous Markov Chains, could be viewed as but one of a number of different types of semi-norms of suitably defined stochastic matrices. More directly relevant to gossiping, in [12] we've used simple examples to show that the largely ignored problem of devising a gossiping protocol which avoids deadlock while generating rapidly converging gossiping sequences is especially formidable [14]. Nonetheless we devised a deadlock-free protocol which solves the problem.…”

“…In some applications, this requirement may be difficult to satisfy. To deal we this, we've also devised a new, provably correct deterministic gossiping-like protocol which solves the distributed averaging problem without requiring any assumptions about the times at which agents and their neighbors place requests to gossip [14]. The protocol is deadlock-free, does not require broadcasting, and leads to consensus exponentially fast.…”