Space Complexity of Self-Stabilizing Leader Election in Population Protocol Based on k-Interaction

Abstract

Population protocol (PP) is a distributed computing model for passively mobile systems, in which a computation is executed by interactions between two agents. This paper is concerned with an extended model, population protocol based on interactions of at most k agents (PP k ). Beauquier et al. (2012) recently introduced the model, and showed a hierarchy of computational powers of PP k with respect toak; a PP k + 1 is strictly more powerful than a PP k . Motivated by a further understanding of the model, this paper investigates the space complexity of PP k for self-stabilizing leader election (SS-LE), which is a fundamental problem for a distributed system. Cai et al. (2012) showed that the space complexity of SS-LE for n agents by a PP (i.e., PP2) is exactly n. This paper shows that the space complexity of SS-LE for n agents by a PP k is exactly i¾?(n '—' 1)/(k '—' 1)i¾? + 1.