Non asymptotic bounds in asynchronous sum-weight gossip protocols

TL;DR

This paper derives probabilistic bounds on the message complexity for asynchronous gossip protocols to reach consensus, providing explicit formulas for fully connected graphs and spectral approximations for general graphs.

Contribution

It introduces non-asymptotic probabilistic bounds on diffusion time in asynchronous gossip protocols, including explicit formulas and spectral approximations.

Findings

Explicit formula for fully connected graphs.

Spectral approximation for general graphs.

Probabilistic bounds on message complexity.

Abstract

This paper focuses on non-asymptotic diffusion time in asynchronous gossip protocols. Asynchronous gossip protocols are designed to perform distributed computation in a network of nodes by randomly exchanging messages on the associated graph. To achieve consensus among nodes, a minimal number of messages has to be exchanged. We provides a probabilistic bound to such number for the general case. We provide a explicit formula for fully connected graphs depending only on the number of nodes and an approximation for any graph depending on the spectrum of the graph.