Loosely-Stabilizing Leader Election in Population Protocol Model

Lecture Notes in Computer Science

Kakugawa

et al. 2014

Self Cite

We consider the leader election problem in population protocol models. In pragmatic settings of population protocols, self-stabilization is a highly desired feature owing to its fault resilience and the benefit of initialization freedom. However, the design of self-stabilizing leader election is possible only under a strong assumption (i.e., the knowledge of the exact size of a network) and rich computational resource (i.e., the number of states). Loose-stabilization, introduced by Sudo et al. [Theoretical Computer Science, 2012], is a promising relaxed concept of selfstabilization to address the aforementioned issue. Loose-stabilization guarantees that starting from any configuration, the network will reach a safe configuration where a single leader exists within a short time, and thereafter it will maintain the single leader for a long time, but not forever. The main contribution of the paper is a time-optimal loosely-stabilizing leader election protocol. While the shortest convergence time achieved so far in loosely-stabilizing leader election is O(log 3 n) parallel time, the proposed protocol with design parameter τ ≥ 1 attains O(τ log n) parallel convergence time and Ω(n τ ) parallel holding time (i.e., the length of the period keeping the unique leader), both in expectation. This protocol is time-optimal in the sense of both the convergence and holding times in expectation because any loosely-stabilizing leader election protocol with the same length of the holding time is known to require Ω(τ log n) parallel time.

Section: Countdown With Higher Value Propagationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Loosely-Stabilizing Leader Election on Arbitrary Graphs in Population Protocols

Lecture Notes in Computer Science

Kakugawa

et al. 2014

Self Cite

“…To solve SS-LE in a more practical way, our previous work [14] introduces the concept of loose-stabilization, which relaxes the closure requirement of self-stabilization but keeps its advantage in practice. Specifically, starting from any initial configuration, the population must reach a safe configuration within a relatively short time; after that, the specification of the problem (the unique leader for leader election) must be sustained for a sufficiently long time, though not necessarily forever.…”

Section: Introductionmentioning

confidence: 99%

“…Specifically, starting from any initial configuration, the population must reach a safe configuration within a relatively short time; after that, the specification of the problem (the unique leader for leader election) must be sustained for a sufficiently long time, though not necessarily forever. In [14], we gave a loosely-stabilizing leader election (LS-LE) protocol assuming that every agent knows a common upper bound N of n. This protocol is practically equivalent to an SS-LE protocol since it maintains the unique leader for exponential time in n (that is, practically forever) after reaching a safe configuration within O(N log N ) parallel time, which we will define later. The assumption that we can use an upper bound N of n is practical because the protocol works correctly even if we make a large overestimation of n, such as N = 10n.…”

Section: Introductionmentioning

confidence: 99%

Loosely-stabilizing leader election with polylogarithmic convergence time

Theoretical Computer Science

Kakugawa

et al. 2020

Self Cite

A loosely-stabilizing leader election protocol with polylogarithmic convergence time in the population protocol model is presented in this paper. In the population protocol model, which is a common abstract model of mobile sensor networks, it is known to be impossible to design a self-stabilizing leader election protocol. Thus, in our prior work, we introduced the concept of loose-stabilization, which is weaker than self-stabilization but has similar advantage as selfstabilization in practice. Following this work, several loosely-stabilizing leader election protocols are presented. The loosely-stabilizing leader election guarantees that, starting from an arbitrary configuration, the system reaches a safe configuration with a single leader within a relatively short time, and keeps the unique leader for an sufficiently long time thereafter. The convergence times of all the existing loosely-stabilizing protocols, i.e., the expected time to reach a safe configuration, are polynomial in n where n is the number of nodes (while the holding times to keep the unique leader are exponential in n). In this paper, a loosely-stabilizing protocol with polylogarithmic convergence time is presented. Its holding time is not exponential, but arbitrarily large polynomial in n.

Logarithmic Expected-Time Leader Election in Population Protocol Model

Lecture Notes in Computer Science

Izumi

et al. 2019

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In this paper, we present the first leader election protocol in the population protocol model that stabilizes O(log n) parallel time in expectation with O(log n) states per agent, where n is the number of agents. Given a rough knowledge m of the population size n such that m ≥ log 2 n and m = O(log n), the proposed protocol guarantees that exactly one leader is elected and the unique leader is kept forever thereafter.