Efficient Counting with Optimal Resilience

Lenzen, Christoph; Rybicki, Joel

doi:10.1007/978-3-662-48653-5_2

Cited by 9 publications

(18 citation statements)

References 13 publications

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“…Our approach bears similarity to our constructions from earlier work [26,28], but attains better bit complexity and can be used with an arbitrary consensus routine. On a high level, we take the following approach as also illustrated in Figure 4: 1.…”

Section: Constructing Weak Pulsers From Less Resilient Strong Pulsersmentioning

confidence: 95%

“…Recently, we gave recursive constructions that achieve linear stabilisation time using only polylogarithmic message size and state bits per node [26,28]; see also the extended and revised version [29]. However, our previous constructions relied on specific (deterministic) consensus routines and their properties in a relatively ad hoc manner.…”

Section: Related Workmentioning

confidence: 99%

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Near-optimal self-stabilising counting and firing squads

Lenzen

Rybicki

2018

Distrib. Comput.

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Consider a fully-connected synchronous distributed system consisting of n nodes, where up to f nodes may be faulty and every node starts in an arbitrary initial state. In the synchronous C-counting problem, all nodes need to eventually agree on a counter that is increased by one modulo C in each round for given C > 1. In the self-stabilising firing squad problem, the task is to eventually guarantee that all non-faulty nodes have simultaneous responses to external inputs: if a subset of the correct nodes receive an external "go" signal as input, then all correct nodes should agree on a round (in the not-too-distant future) in which to jointly output a "fire" signal. Moreover, no node should generate a "fire" signal without some correct node having previously received a "go" signal as input.We present a framework reducing both tasks to binary consensus at very small cost. For example, we obtain a deterministic algorithm for self-stabilising Byzantine firing squads with optimal resilience f < n/3, asymptotically optimal stabilisation and response time O(f ), and message size O(log f ). As our framework does not restrict the type of consensus routines used, we also obtain efficient randomised solutions, and it is straightforward to adapt our framework for other types of permanent faults.1 Current affiliation of JR.

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Section: Constructing Weak Pulsers From Less Resilient Strong Pulsersmentioning

confidence: 95%

Section: Related Workmentioning

confidence: 99%

Near-optimal self-stabilising counting and firing squads

Lenzen

Rybicki

2018

Distrib. Comput.

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“…(E.g., agents regularly receive a common pulse.) Clock synchronization in this setting is often referred to as digital clock synchronization, or synchronous counting [13,19,33,34]. The focus of most previous work on this problem has been to achieve resilience against Byzantine agents, whose behaviour can be arbitrary (and malicious), along with self-stabilization, which guarantees convergence from any configuration of the agents' states (and thus resilience to transient failures).…”

Section: Introductionmentioning

confidence: 99%

Self-Stabilizing Clock Synchronization with 1-bit Messages

Bastide¹,

Giakkoupis²,

Saribekyan³

2021

Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms (SODA)

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We study the fundamental problem of distributed clock synchronization in a basic probabilistic communication setting. We consider a synchronous fully-connected network of n agents, where each agent has a local clock, that is, a counter increasing by one modulo T in each round. The clocks have arbitrary values initially, and they must all indicate the same time eventually. We assume a pull communication model, where in every round each agent receives an -bit message from a random agent. We devise several fast synchronization algorithms that use small messages and are self-stabilizing, that is, the complete initial state of each agent (not just its clock value) can be arbitrary.We first provide a surprising algorithm for synchronizing a binary clock (T = 2) using 1-bit messages ( = 1). This is a variant of the voter model and converges in O(log n) rounds w.h.p., unlike the voter model which needs polynomial time. Next we present an elegant extension of our algorithm that synchronizes a modulo T = 4 clock, with = 1, in O(log n) rounds. Using these two algorithms, we refine an algorithm of Boczkowski et al. (SODA'17), that synchronizes a modulo T clock in polylogarithmic time (in n and T ). The original algorithm uses = 3 bit messages, and each agent receives messages from two agents per round. Our algorithm reduces the message size to = 2, and the number of messages received to one per round, without increasing the running time. Finally, we present two algorithms that simulate our last algorithm achieving < 2, without hurting the asymptotic running time. The first algorithm uses a message space of size 3, i.e., = log 2 (3). The second requires a rough upper bound on log n, and uses just 1-bit messages. More generally, our constructions can simulate any self-stabilizing algorithm that requires a shared clock, without increasing the message size and by only increasing the running time by a constant factor and a polylogarithmic term.

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“…Moreover, we present two complementary approaches for reducing the number of bits communicated during and after stabilisation. * The manuscript is an extended and revised version of two preliminary conference reports [24,26] that appeared in the is based on, we outlined a recursive approach where each node needs to participate in only O(log f / log log f ) parallel instances of consensus. However, this approach resulted in suboptimal resilience of f = n 1−o(1) .Finally, we note that while counting algorithms are usually designed for the case of a fullyconnected communication topology, the algorithms can be extended to use in a variety of other graph classes with high enough connectivity [16].Related problems.…”

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Efficient Counting with Optimal Resilience

Lenzen¹,

Rybicki²,

Suomela³

2017

SIAM J. Comput.

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Abstract. Consider a complete communication network of n nodes, where the nodes receive a common clock pulse. We study the synchronous c-counting problem: given any starting state and up to f faulty nodes with arbitrary behaviour, the task is to eventually have all correct nodes labeling the pulses with increasing values modulo c in agreement. Thus, we are considering algorithms that are self-stabilising despite Byzantine failures. In this work, we give new algorithms for the synchronous counting problem that (1) are deterministic, (2) have optimal resilience, (3) have a linear stabilisation time in f (asymptotically optimal), (4) use a small number of states, and consequently, (5) communicate a small number of bits per round. Prior algorithms either resort to randomisation, use a large number of states and need high communication bandwidth, or have suboptimal resilience. In particular, we achieve an exponential improvement in both state complexity and message size for deterministic algorithms. Moreover, we present two complementary approaches for reducing the number of bits communicated during and after stabilisation. * The manuscript is an extended and revised version of two preliminary conference reports [24,26] that appeared in the

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Efficient Counting with Optimal Resilience

Cited by 9 publications

References 13 publications

Near-optimal self-stabilising counting and firing squads

Near-optimal self-stabilising counting and firing squads

Self-Stabilizing Clock Synchronization with 1-bit Messages

Efficient Counting with Optimal Resilience

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