TY - JOUR
T1 - Loosely-stabilizing leader election in a population protocol model
AU - Sudo, Yuichi
AU - Nakamura, Junya
AU - Yamauchi, Yukiko
AU - Ooshita, Fukuhito
AU - Kakugawa, Hirotsugu
AU - Masuzawa, Toshimitsu
N1 - Funding Information:
This work is supported in part by Global COE Program of MEXT, Grant-in-Aid for Scientific Research ((B)17300020, (B)22300009, (B)20300012) of JSPS, Grant-in-Aid for Young Scientists ((B)18700059) of JSPS, and the Kayamori Foundation of Informational Science Advancement.
PY - 2012/7/27
Y1 - 2012/7/27
N2 - 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 Ω(N eN) 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.
AB - 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 Ω(N eN) 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.
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U2 - 10.1016/j.tcs.2012.01.007
DO - 10.1016/j.tcs.2012.01.007
M3 - Article
AN - SCOPUS:84862026842
VL - 444
SP - 100
EP - 112
JO - Theoretical Computer Science
JF - Theoretical Computer Science
SN - 0304-3975
ER -