A Population Protocol for Uniform $k$-partition under Global Fairness

Abstract

In this paper, we consider a uniform k-partition problem in a population protocol model. The uniform k-partition problem divides a population into k groups of the same size. For this problem, we give a symmetric protocol with designated initial states under global fairness. The proposed protocol requires 3k-2 states for each agent. Since any protocol for the uniform k-partition problem requires ?(k) states to indicate a group, the space complexity of the proposed protocol is asymptotically optimal.