Time-Optimal Self-stabilizing Leader Election on Rings in Population Protocols

Yokota, Daisuke; Sudo, Yuichi; Masuzawa, Toru

doi:10.1007/978-3-030-64348-5_24

Cited by 6 publications

(2 citation statements)

References 21 publications

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“…While this paper considers only the complete graph (the most difficult case), other work considers protocols that assume a particular non-complete graph topology. In rings and regular graphs with constant degree, SSLE is feasible even with only a constant state space [10,25,26,60]. In another recent related work [57], the authors study the feasibility requirements of SSLE in arbitrary graphs, as well as the problem of ranking that we also study (see below).…”

Section: Problem Variantsmentioning

confidence: 99%

Time-Optimal Self-Stabilizing Leader Election in Population Protocols

Burman

Chen

et al. 2021

Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing

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We consider the standard population protocol model, where (a priori) indistinguishable and anonymous agents interact in pairs according to uniformly random scheduling. The self-stabilizing leader election problem requires the protocol to converge on a single leader agent from any possible initial configuration. We initiate the study of time complexity of population protocols solving this problem in its original setting: with probability 1, in a complete communication graph. The only previously known protocol by Cai, Izumi, and Wada [Theor. Comput. Syst. 50] runs in expected parallel time Θ( 2 ) and has the optimal number of states in a population of agents. The existing protocol has the additional property that it becomes silent, i.e., the agents' states eventually stop changing.Observing that any silent protocol solving self-stabilizing leader election requires Ω( ) expected parallel time, we introduce a silent protocol that uses optimal ( ) parallel time and states. Without any silence constraints, we show that it is possible to solve self-stabilizing leader election in asymptotically optimal expected parallel time of (log ), but using at least exponential states (a quasipolynomial number of bits). All of our protocols (and also that of Cai et al.) work by solving the more difficult ranking problem: assigning agents the ranks 1, . . . , .

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Section: Problem Variantsmentioning

confidence: 99%

Time-Optimal Self-Stabilizing Leader Election in Population Protocols

Burman

Chen

et al. 2021

Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing

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“…Later, they gave a protocol for d-regular graphs using O(d 12 ) states [27]. Recently, Yokota, Sudo and Toshimitsu [55] reported a leader election protocol for directed cycles that runs in O(n) parallel time using O(N n) states, where N ≥ n is a known upper bound on the population size.…”

Section: Population Protocolsmentioning

confidence: 99%

Fast Graphical Population Protocols

Alistarh,

Gelashvili,

Rybicki

2021

Preprint

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Let G be a graph on n nodes. In the stochastic population protocol model, a collection of n indistinguishable, resource-limited nodes collectively solve tasks via pairwise interactions. In each interaction, two randomly chosen neighbors first read each other's states, and then update their local states. A rich line of research has established tight upper and lower bounds on the complexity of fundamental tasks, such as majority and leader election, in this model, when G is a clique. Specifically, in the clique, these tasks can be solved fast, i.e., in n polylog n pairwise interactions, with high probability, using at most polylog n states per node.In this work, we consider the more general setting where G is an arbitrary graph, and present a technique for simulating protocols designed for fully-connected networks in any connected regular graph. Our main result is a simulation that is efficient on many interesting graph families: roughly, the simulation overhead is polylogarithmic in the number of nodes, and quadratic in the conductance of the graph. As a sample application, we show that, in any regular graph with conductance φ, both leader election and exact majority can be solved in φ −2 • n polylog n pairwise interactions, with high probability, using at most φ −2 • polylog n states per node. This shows that there are fast and space-efficient population protocols for leader election and exact majority on graphs with good expansion properties. We believe our results will prove generally useful, as they allow efficient technology transfer between the well-mixed (clique) case, and the under-explored spatial setting.

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