Average-Consensus Algorithms in a Deterministic Framework

TL;DR

This paper introduces four deterministic algorithms for average consensus in multi-node networks with delays, providing conditions for convergence, resource cost analysis, and empirical performance comparisons.

Contribution

It presents four new deterministic average-consensus algorithms with proven communication conditions and resource cost analysis in a delayed, directed network setting.

Findings

All four algorithms achieve consensus under specified conditions.

Resource costs are quantified in terms of communication and storage.

Empirical results show competitive convergence rates compared to gossip algorithms.

Abstract

We consider the average-consensus problem in a multi-node network of finite size. Communication between nodes is modeled by a sequence of directed signals with arbitrary communication delays. Four distributed algorithms that achieve average-consensus are proposed. Necessary and sufficient communication conditions are given for each algorithm to achieve average-consensus. Resource costs for each algorithm are derived based on the number of scalar values that are required for communication and storage at each node. Numerical examples are provided to illustrate the empirical convergence rate of the four algorithms in comparison with a well-known "gossip" algorithm as well as a randomized information spreading algorithm when assuming a fully connected random graph with instantaneous communication.