Self-Stabilizing Clock Synchronization in Probabilistic Networks
We consider the fundamental problem of clock synchronization in a synchronous multi-agent system. Each agent holds a clock with an arbitrary initial value, and clocks must eventually indicate the same value, modulo some integer P. A known solution for this problem in dynamic networks is the self-stabilization SAP (for self-adaptive period) algorithm, which uses finite memory and relies solely on the assumption of a finite dynamic diameter in the communication network.
This paper extends the results on this algorithm to probabilistic communication networks: We introduce the concept of strong connectivity with high probability and we demonstrate that in any probabilistic communication network satisfying this hypothesis, the SAP algorithm synchronizes clocks with high probability. The proof of such a probabilistic hyperproperty is based on novel tools and relies on weak assumptions about the probabilistic communication network, making it applicable to a wide range of networks, including the classical push model. We provide an upper bound on time and space complexity.
Building upon previous works by Feige et al. and Pittel, the paper provides solvability results and evaluates the stabilization time and space complexity of SAP in two specific cases of communication topologies.
Self-stabilization
Clock synchronization
Probabilistic networks
Theory of computation~Distributed algorithms
Theory of computation~Dynamic graph algorithms
12:1-12:18
Regular Paper
We would like to thank Patrick Lambein-Monette, Stephan Merz, and Guillaume Prémel for very useful discussions.
Bernadette
Charron-Bost
Bernadette Charron-Bost
DI ENS, École Normale Supérieure, 75005 Paris, France
Louis
Penet de Monterno
Louis Penet de Monterno
École polytechnique, IP Paris, 91128 Palaiseau, France
10.4230/LIPIcs.DISC.2023.12
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Bernadette Charron-Bost and Louis Penet de Monterno
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