Space complexity of self-stabilizing leader election in passively-mobile anonymous agents

Authors:
Shukai Cai;Taisuke Izumi;Koichi Wada
Affiliations:
Graduate School of Engineering, Nagoya Institute of Technology, Nagoya, Japan;Graduate School of Engineering, Nagoya Institute of Technology, Nagoya, Japan;Graduate School of Engineering, Nagoya Institute of Technology, Nagoya, Japan
Venue:
SIROCCO'09 Proceedings of the 16th international conference on Structural Information and Communication Complexity
Year:
2009

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Abstract

A population protocol is one of distributed computing models for passively-mobile systems, where a number of agents change their states by pairwise interactions between two agents. In this paper, we investigate the solvability of the self-stabilizing leader election in population protocols without any kind of oracles. We identify the necessary and sufficient condition to solve the self-stabilizing leader election in population protocols from the aspects of local memory complexity and fairness assumptions. This paper shows that under the assumption of global fairness, no protocol using only n−1 states can solve the self-stabilizing leader election in complete interaction graphs, where n is the number of agents in the system. To prove this impossibility, we introduce a novel proof technique, called closed-set argument. In addition, we propose a self-stabilizing leader election protocol using n states that works even under the unfairness assumption. This protocol requires the exact knowledge about the number of agents in the system. We also show that such knowledge is necessary to construct any self-stabilizing leader election protocol.