Space Complexity of Self-Stabilizing Leader Election in Population Protocol Based on k-Interaction
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 to k; 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 ⌈(n − 1)/(k − 1)⌉ + 1.
Unable to display preview. Download preview PDF.
- 4.Angluin, D., Aspnes, J., Fischer, M.J., Jiang, H.: Self-stabilizing population protocols. ACM Transactions on Autonomous and Adaptive Systems 3, Article 13 (2008)Google Scholar
- 7.Beauquier, J., Clement, J., Messika, S., Rosaz, L., Rozoy, B.: Self-stabilizing counting in mobile sensor networks. In: Proc. of PODC 2007, pp. 396–397 (2007)Google Scholar
- 9.Canepa, D., Potop-Butucaru, M.G.: Stabilizing leader election in population protocols. INRIA Rocquencourt, RR-6269 (2007), http://hal.inria.fr/inria-00166632/en/
- 12.Devismes, S., Tixeuil, S., Yamashita, M.: Weak vs. self vs. probabilistic stabilization. In: Proc. of ICDCS 2008, pp. 681–688 (2008)Google Scholar
- 18.Schrijver, A.: Combinatorial Optimization. Springer (2003)Google Scholar