Distributed Consensus with Finite Message Passing

TL;DR

This paper investigates the limits and optimal strategies for distributed consensus in dynamic networks with finite message passing, providing conditions, characterizations, and asymptotic results for conflict minimization.

Contribution

It introduces a sufficient condition for conflict-free consensus after R rounds, characterizes optimal protocols for path graphs, and analyzes conflict reduction as resources grow.

Findings

No protocol guarantees conflict-free allocation after R rounds under certain conditions.

Random allocation minimizes conflicts in path graphs without message passing.

Conflicts decrease to zero as resources increase.

Abstract

Inspired by distributed resource allocation problems in dynamic topology networks, we initiate the study of distributed consensus with finite messaging passing. We first find a sufficient condition on the network graph for which no distributed protocol can guarantee a conflict-free allocation after $R$ rounds of message passing. Secondly we fully characterize the conflict minimizing zero-round protocol for path graphs, namely random allocation, which partitions the graph into small conflict groups. Thirdly, we enumerate all one-round protocols for path graphs and show that the best one further partitions each of the smaller groups. Finally, we show that the number of conflicts decrease to zero as the number of available resources increase.