How to Prove Impossibility Under Global Fairness: On Space Complexity of Self-Stabilizing Leader Election on a Population Protocol Model

Cai, Shukai; Izumi, Taisuke; Wada, Koichi

doi:10.1007/s00224-011-9313-z

Cited by 50 publications

(68 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [25] unique IDs are assumed, and it is shown how to compute functions tolerating a bounded number of Byzantine faults, under the assumption that Byzantine agents cannot forge IDs. Self-stabilizing solutions have been devised for specific problems such as leader election (assuming knowledge of the system's size and a non-constant number of states [12], or assuming a leader detection oracle [23]) and counting (assuming the presence of a leader [9]). Moreover, in [10] a self-stabilizing transformer for general protocols has been studied in a slightly different model and under the assumption of unbounded memory and a leader.…”

Section: Related Workmentioning

confidence: 99%

On the Power of Weaker Pairwise Interaction: Fault-Tolerant Simulation of Population Protocols

Luna

Flocchini

Izumi

et al. 2017

2017 IEEE 37th International Conference on Distributed Computing Systems (ICDCS)

Self Cite

View full text Add to dashboard Cite

In this paper we investigate the computational power of Population Protocols (PP) under some unreliable and/or weaker interaction models. More precisely, we focus on two features related to the power of interactions: omission failures and one-way communications. An omission failure, a notion that this paper introduces for the first time in the context of PP, is the loss by one or both parties of the information transmitted in an interaction. The failure may or may not be detected by either party. On the other hand, in one-way models, communication happens only in one direction: only one of the two agents can change its state depending on both agents' states, and the other agent may or may not be aware of the interaction. These notions can be combined, obtaining one-way protocols with (possibly detectable) omission failures.A general question is what additional power is necessary and sufficient to completely overcome the weakness of one-way protocols and enable them to simulate two-way protocols, with and without omission failures. As a basic feature, a simulator needs to implement an atomic communication of states between two agents; this task is further complicated by the anonymity of the agents, their lack of knowledge of the system, and the limited amount of memory that they may have.We provide the first answers to these questions by presenting and analyzing several simulators, i.e., wrapper protocols converting any protocol for the standard two-way model into one running on a weaker one.

show abstract

Section: Related Workmentioning

confidence: 99%

On the Power of Weaker Pairwise Interaction: Fault-Tolerant Simulation of Population Protocols

Luna

Flocchini

Izumi

et al. 2017

2017 IEEE 37th International Conference on Distributed Computing Systems (ICDCS)

Self Cite

View full text Add to dashboard Cite

show abstract

“…Cai et al [7] show that, in complete communication graphs, n agent-states are necessary and su cient to solve SSLE, where n is the population size. This result involves that an oracle is necessary for solving SSLE in population protocols.…”

Section: Related Workmentioning

confidence: 99%

“…They prove that Ω? helps to solve SSLE in complete graphs and on rings, while the same problem in complete graphs is proven impossible without oracles [4,7]. After the introduction of Ω?, other oracles for leader election in population protocols appeared in the literature, all based on some information related to global con gurations.…”

Section: Introductionmentioning

confidence: 99%

Self-stabilizing Leader Election in Population Protocols over Arbitrary Communication Graphs

Beauquier

Blanchard

Burman

2013

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. This paper considers the fundamental problem of self-stabilizing leader election (SSLE) in the model of population protocols. In this model, an unknown number of asynchronous, anonymous and nite state mobile agents interact in pairs over a given communication graph. SSLE has been shown to be impossible in the original model. This impossibility can been circumvented by a modular technique augmenting the system with an oracle -an external module abstracting the added assumption about the system. Fischer and Jiang have proposed solutions to SSLE, for complete communication graphs and rings, using an oracle Ω?, called the eventual leader detector. In this work, we present a solution for arbitrary graphs, using a composition of two copies of Ω?. We also prove that the di culty comes from the requirement of self-stabilization, by giving a solution without oracle for arbitrary graphs, when an uniform initialization is allowed. Finally, we prove that there is no self-stabilizing implementation of Ω? using SSLE, in a sense we de ne precisely.

show abstract

“…This problem requires that (i) starting from any configuration, a population reaches a safe configuration in which exactly one leader exists; and thereafter, (ii) it keeps this leader forever. These requirements guarantee tolerance against finitely [12] [24] LS-LE n ≤ N = poly(n) O(τ log 3 n) Ω(n τ ) O(τ 2 log 5 n) any τ ≥ 10 ours LS-LE n ≤ N = poly(n) O(τ log n) Ω(n τ ) O(τ log n) any τ ≥ 1 many transient faults. Since many protocols (self-stabilizing or non-self-stabilizing) in the literature assume a unique leader [5,7,6], SS-LE is key to improving fault-tolerance of the PP model itself.…”

Section: Introductionmentioning

confidence: 99%

“…Since many protocols (self-stabilizing or non-self-stabilizing) in the literature assume a unique leader [5,7,6], SS-LE is key to improving fault-tolerance of the PP model itself. However, it is known that no protocol can solve SS-LE unless every agent in the population knows the exact size n of the population [7,12] 1 . Under this strong assumption (i.e., all agents know exact n), several SS-LE protocols have been presented in the literature.…”

Section: Introductionmentioning

confidence: 99%

Loosely-Stabilizing Leader Election on Arbitrary Graphs in Population Protocols

Sudo

Ooshita

Kakugawa

et al. 2014

Lecture Notes in Computer Science

View full text Add to dashboard 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.

show abstract

How to Prove Impossibility Under Global Fairness: On Space Complexity of Self-Stabilizing Leader Election on a Population Protocol Model

Cited by 50 publications

References 6 publications

On the Power of Weaker Pairwise Interaction: Fault-Tolerant Simulation of Population Protocols

On the Power of Weaker Pairwise Interaction: Fault-Tolerant Simulation of Population Protocols

Self-stabilizing Leader Election in Population Protocols over Arbitrary Communication Graphs

Loosely-Stabilizing Leader Election on Arbitrary Graphs in Population Protocols

Contact Info

Product

Resources

About