Loosely-stabilizing leader election in a population protocol model

Authors:
Yuichi Sudo;Junya Nakamura;Yukiko Yamauchi;Fukuhito Ooshita;Hirotsugu Kakugawa;Toshimitsu Masuzawa
Affiliations:
Graduate School of Information Science and Technology, Osaka University, 1-5 Yamadaoka, Suita, Osaka, 565-0871, Japan;Graduate School of Information Science and Technology, Osaka University, 1-5 Yamadaoka, Suita, Osaka, 565-0871, Japan;Graduate School of Information Science and Electrical Engineering, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan;Graduate School of Information Science and Technology, Osaka University, 1-5 Yamadaoka, Suita, Osaka, 565-0871, Japan;Graduate School of Information Science and Technology, Osaka University, 1-5 Yamadaoka, Suita, Osaka, 565-0871, Japan;Graduate School of Information Science and Technology, Osaka University, 1-5 Yamadaoka, Suita, Osaka, 565-0871, Japan
Venue:
Theoretical Computer Science
Year:
2012

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Abstract

A self-stabilizing protocol guarantees that starting from any arbitrary initial configuration, a system eventually comes to satisfy its specification and keeps the specification forever. Although self-stabilizing protocols show excellent fault-tolerance against any transient faults (e.g. memory crash), designing self-stabilizing protocols is difficult and, what is worse, might be impossible due to the severe requirements. To circumvent the difficulty and impossibility, we introduce a novel notion of loose-stabilization, that relaxes the closure requirement of self-stabilization; starting from any arbitrary configuration, a system comes to satisfy its specification in a relatively short time, and it keeps the specification not forever but for a long time. To show the effectiveness and feasibility of this new concept, we present a probabilistic loosely-stabilizing leader election protocol in the Probabilistic Population Protocol (PPP) model of complete networks. Starting from any configuration, the protocol elects a unique leader within O(nNlogn) expected steps and keeps the unique leader for @W(Ne^N) expected steps, where n is the network size (not known to the protocol) and N is a known upper bound of n. This result proves that introduction of the loose-stabilization circumvents the already-known impossibility result; the self-stabilizing leader election problem in the PPP model of complete networks cannot be solved without the knowledge of the exact network size.