Uniform Bipartition in the Population Protocol Model with Arbitrary Communication Graphs

TL;DR

This paper investigates the uniform bipartition problem in population protocols with arbitrary communication graphs, analyzing solvability under various assumptions and providing protocols with tight space complexity when feasible.

Contribution

It clarifies the conditions for solvability of uniform bipartition with arbitrary graphs and presents protocols with optimal space complexity under global fairness.

Findings

Solvability depends on initial states, presence of a base station, and fairness assumptions.

Protocols are provided for cases where bipartition is achievable.

Space complexity is proven to be tight under global fairness.

Abstract

In this paper, we focus on the uniform bipartition problem in the population protocol model. This problem aims to divide a population into two groups of equal size. In particular, we consider the problem in the context of \emph{arbitrary} communication graphs. As a result, we clarify the solvability of the uniform bipartition problem with arbitrary communication graphs when agents in the population have designated initial states, under various assumptions such as the existence of a base station, symmetry of the protocol, and fairness of the execution. When the problem is solvable, we present protocols for uniform bipartition. When global fairness is assumed, the space complexity of our solutions is tight.