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

• Published in: Stabilization, Safety, and Security of Distributed Systems pp. 86 - 97
• Main Authors: Xu, Xiaoguang, Yamauchi, Yukiko, Kijima, Shuji, Yamashita, Masafumi
• Format: Book Chapter
• Language: English
• Published: Cham Springer International Publishing
• Series: Lecture Notes in Computer Science
• ISBN: 9783319030883; 3319030884
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-319-03089-0_7

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 (PPk). Beauquier et al. (2012) recently introduced the model, and showed a hierarchy of computational powers of PPk with respect to k; a PPk + 1 is strictly more powerful than a PPk. Motivated by a further understanding of the model, this paper investigates the space complexity of PPk 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 PPk is exactly ⌈(n − 1)/(k − 1)⌉ + 1.