Election in partially anonymous networks with arbitrary knowledge in message passing systems

Chalopin, Jérémie; Godard, Emmanuel; Métivier, Yves

doi:10.1007/s00446-012-0163-y

Cited by 16 publications

(13 citation statements)

References 21 publications

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“…Mostly related to this paper is the work of Yamashita and Kameda [26], which fully characterize the solvability of deterministic leader election over general graphs in the message-passing model; their characterization follows from considering various types of symmetries in the graph. Other characterization appeared in [5,7,8].…”

Section: Related Workmentioning

confidence: 99%

The Topology of Randomized Symmetry-Breaking Distributed Computing

Fraigniaud

Gelles

Lotker

2021

Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing

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Studying distributed computing through the lens of algebraic topology has been the source of many significant breakthroughs during the last two decades, especially in the design of lower bounds or impossibility results for deterministic algorithms. In a nutshell, this approach consists of capturing all the possible states of a distributed system at a certain time as a simplicial complex called protocol complex, and viewing computation as a simplicial map from that complex to the so-called output complex, that captures all possible legal output states of the system.This paper aims at studying randomized synchronous distributed computing through the lens of algebraic topology. We do so by studying the wide class of (input-free) symmetry-breaking tasks, e.g., leader election, in synchronous fault-free anonymous systems. We show that it is possible to redefine solvability of a task "locally", i.e., for each simplex of the protocol complex individually, without requiring any global consistency. However, this approach has a drawback: it eliminates the topological aspect of the computation, since a single facet has a trivial topological structure. To overcome this issue, we introduce a "projection" of both protocol and output complexes, where every simplex is mapped to a complex ( ); the later has a rich structure that replaces the structure we lost by considering one single facet at a time.To show the significance and applicability of our topological approach, we derive necessary and sufficient conditions for solving leader election in synchronous fault-free anonymous sharedmemory and message-passing models. In both models, we consider scenarios in which there might be correlations between the random values provided to the nodes. In particular, different parties might have access to the same randomness source so their randomness is not independent but equal. Interestingly, we find that solvability of leader election relates to the number of parties that possess correlated randomness, either directly or via their greatest common divisor, depending on the specific communication model.

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Section: Related Workmentioning

confidence: 99%

The Topology of Randomized Symmetry-Breaking Distributed Computing

Fraigniaud

Gelles

Lotker

2021

Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing

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“…The main ideas of the election algorithm developed in [37] were applied to some other models in [15,16,13] by adapting the notion of covering. A characterisation of families of graphs which admit an election algorithm (i.e., the same algorithm works on each graph of the family) can be found in [14].…”

Section: Further Related Workmentioning

confidence: 99%

Deterministic Leader Election Takes $$\Theta (D + \log n)$$ Θ ( D + log n ) Bit Rounds

et al. 2018

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Leader election is, together with consensus, one of the most central problems in distributed computing. This paper presents a distributed algorithm, called ST T , for electing deterministically a leader in an arbitrary network, assuming processors have unique identifiers of size O(log n), where n is the number of processors. It elects a leader in O(D + log n) rounds, where D is the diameter of the network, with messages of size O(1). Thus it has a bit round complexity of O(D + log n). This substantially improves upon the best known algorithm whose bit round complexity is O(D log n). In fact, using the lower bound by Kutten et al. (2015) and a result of Dinitz and Solomon (2007), we show that the bit round complexity of ST T is optimal (up to a constant factor), which is a significant step forward in understanding the interplay between time and message optimality for the election problem. Our algorithm requires no knowledge on the graph such as n or D, and the pipelining technique we introduce to break the O(D log n) barrier is general. This research has been partially supported by ANR projects DESCARTES and ESTATE (resp. ANR-16-CE40-0023 and ANR-16-CE25-0009-03). A preliminary subset of this work appeared in the proceedings of DISC 2016 [12].

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“…The problem of describing which arbitrary knowledge enables to solve the Election Problem was introduced in [GM02], where it is solved for a specific model. It has been solved for the standard message passing model in [CGM12]. These papers use quasi-simulation techniques introduced in [MMW97] but contrary to the model investigated in [YK96b,BV99,CGM12], it should be noted that unknown participants networks are communication networks where the difficulty arises from asynchrony and not from synchronous executions.…”

Section: Introductionmentioning

confidence: 99%

“…It has been solved for the standard message passing model in [CGM12]. These papers use quasi-simulation techniques introduced in [MMW97] but contrary to the model investigated in [YK96b,BV99,CGM12], it should be noted that unknown participants networks are communication networks where the difficulty arises from asynchrony and not from synchronous executions. It is therefore a qualitatively different model where computability mostly relates to termination detection and not to symmetry breaking.…”

Section: Introductionmentioning

confidence: 99%