Time Complexity of Consensus in Dynamic Networks Under Oblivious Message Adversaries

TL;DR

This paper investigates the time complexity of achieving consensus in dynamic networks with an oblivious message adversary, providing decision procedures, upper and lower bounds, and revealing potential exponential delays.

Contribution

It introduces an explicit decision procedure for consensus solvability under oblivious adversaries and analyzes the associated time complexity bounds for the first time.

Findings

Consensus can require exponentially longer time than simple broadcasting.

The paper provides both upper and lower bounds on consensus time complexity.

Decidability of consensus solvability is established for dynamic directed networks.

Abstract

Consensus is a most fundamental task in distributed computing. This paper studies the consensus problem for a set of processes connected by a dynamic directed network, in which computation and communication is lock-step synchronous but controlled by an oblivious message adversary. In this basic model, determining consensus solvability and designing consensus algorithms in the case where it is possible, has been shown to be surprisingly difficult. We present an explicit decision procedure to determine if consensus is possible under a given adversary. This in turn enables us, for the first time, to study the time complexity of consensus in this model. In particular, we derive time complexity upper bounds for consensus solvability both for a centralized decision procedure as well as for solving distributed consensus. We complement these results with time complexity lower bounds. Intriguingly, we find that reaching consensus under an oblivious message adversary can take exponentially longer than broadcasting the input value of some process to all other processes.