Time-space Trade-offs in Population Protocols for the Majority Problem

TL;DR

This paper introduces new population protocols for the majority problem that improve interaction efficiency and can operate uniformly without prior knowledge of population size, achieving subquadratic stabilization time.

Contribution

It presents novel trade-offs between interaction count and states per agent, improving previous bounds and providing the first uniform protocols with subquadratic stabilization.

Findings

Almost linear improvement in the number of interactions over previous trade-offs.

Protocols can be made uniform, working correctly without knowing the population size.

Achieves subquadratic stabilization time in uniform protocols.

Abstract

Population protocols are a model for distributed computing that is focused on simplicity and robustness. A system of $n$ identical agents (finite state machines) performs a global task like electing a unique leader or determining the majority opinion when each agent has one of two opinions. Agents communicate in pairwise interactions with randomly assigned communication partners. Quality is measured in two ways: the number of interactions to complete the task and the number of states per agent. We present protocols for the majority problem that allow for a trade-off between these two measures. Compared to the only other trade-off result [Alistarh, Gelashvili, Vojnovic; PODC'15], we improve the number of interactions by almost a linear factor. Furthermore, our protocols can be made uniform (working correctly without any information on the population size $n$), yielding the first uniform majority protocols that stabilize in a subquadratic number of interactions.