Request-Based Gossiping without Deadlocks

TL;DR

This paper introduces three deterministic request-based gossiping protocols for distributed averaging, with one guaranteeing deadlock avoidance, another improving efficiency, and a third achieving faster convergence, advancing distributed consensus methods.

Contribution

The paper presents new request-based gossiping protocols that prevent deadlocks, optimize communication, and enhance convergence speed in distributed averaging.

Findings

Second protocol guarantees deadlock avoidance with fewer transmissions

Third protocol achieves significantly faster convergence

A worst-case convergence rate bound is established

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 deadlocks unless careful precautions are taken to ensure that it does not. Many gossiping protocols are request-based which means simply that a gossip between two agents will occur whenever one of the two agents accepts a request to gossip placed by the other. In this paper, we present three deterministic request-based protocols. We show by example that the first can deadlock. The second is guaranteed to avoid deadlocks and requires fewer transmissions per iteration than standard broadcast-based distributed averaging protocols by exploiting the idea of local ordering together with the notion of an agent's neighbor queue; the protocol requires the simplest queue updates, which provides an in-depth understanding of how local ordering and queue updates avoid deadlocks. It is shown that a third protocol which uses a slightly more complicated queue update rule can lead to significantly faster convergence; a worst case bound on convergence rate is provided.