Efficient Counting with Optimal Resilience

Lenzen, Christoph; Rybicki, Joel; Suomela, Jukka

doi:10.1137/16m107877x

Cited by 7 publications

(21 citation statements)

References 30 publications

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“…In contrast, we devise a new recursive scheme that allows us to (1) deterministically generate resynchronisation pulses in Θ(f ) time and (2) probabilistically generate resynchronisation pulses in o(f ) time. To construct algorithms that generate resynchronisation pulses, we employ resilience boosting and ltering techniques inspired by our recent line of work on digital clock synchronisation in the synchronous model [24,26]. One of its main motivations was to gain a be er understanding of the linear time/communication complexity barrier that research on pulse synchronisation ran into, without being distracted by the additional timing uncertainties due to communication delay and clock dri .…”

Section: Contributionsmentioning

confidence: 99%

Self-Stabilising Byzantine Clock Synchronisation Is Almost as Easy as Consensus

Lenzen

Rybicki

2019

J. ACM

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We give fault-tolerant algorithms for establishing synchrony in distributed systems in which each of the n nodes has its own clock. Our algorithms operate in a very strong fault model: we require self-stabilisation, i.e., the initial state of the system may be arbitrary, and there can be up to f < n/3 ongoing Byzantine faults, i.e., nodes that deviate from the protocol in an arbitrary manner. Furthermore, we assume that the local clocks of the nodes may progress at di erent speeds (clock dri ) and communication has bounded delay. In this model, we study the pulse synchronisation problem, where the task is to guarantee that eventually all correct nodes generate well-separated local pulse events (i.e., unlabelled logical clock ticks) in a synchronised manner.Compared to prior work, we achieve exponential improvements in stabilisation time and the number of communicated bits, and give the rst sublinear-time algorithm for the problem:• In the deterministic se ing, the state-of-the-art solutions stabilise in time Θ(f ) and have each node broadcast Θ(f log f ) bits per time unit. We exponentially reduce the number of bits broadcasted per time unit to Θ(log f ) while retaining the same stabilisation time.• In the randomised se ing, the state-of-the-art solutions stabilise in time Θ(f ) and have each node broadcast O(1) bits per time unit. We exponentially reduce the stabilisation time to polylog f while each node broadcasts polylog f bits per time unit. ese results are obtained by means of a recursive approach reducing the above task of self-stabilising pulse synchronisation in the bounded-delay model to non-self-stabilising binary consensus in the synchronous model. In general, our approach introduces at most logarithmic overheads in terms of stabilisation time and broadcasted bits over the underlying consensus routine.

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Section: Contributionsmentioning

confidence: 99%

Self-Stabilising Byzantine Clock Synchronisation Is Almost as Easy as Consensus

Lenzen

Rybicki

2019

J. ACM

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“…This version has earlier been studied in e.g., [13,26,28,29,35,38] under different names, including "digital Clock Synchronization" and "synchronization of phase-clocks"; We simply use the term "Clock Synchronization". There is by now a substantial line of work on Clock Synchronization problems in a self-stabilizing context [27,29,46,45]. We note that in these papers the main focus is on the resilience to Byzantine agents.…”

Section: Related Workmentioning

confidence: 99%

Minimizing message size in stochastic communication patterns: fast self-stabilizing protocols with 3 bits

2018

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This paper considers the basic P U LL model of communication, in which in each round, each agent extracts information from few randomly chosen agents. We seek to identify the smallest amount of information revealed in each interaction (message size) that nevertheless allows for efficient and robust computations of fundamental information dissemination tasks. We focus on the Majority Bit Dissemination problem that considers a population of n agents, with a designated subset of source agents. Each source agent holds an input bit and each agent holds an output bit. The goal is to let all agents converge their output bits on the most frequent input bit of the sources (the majority bit). Note that the particular case of a single source agent corresponds to the classical problem of Broadcast (also termed Rumor Spreading). We concentrate on the severe fault-tolerant context of self-stabilization, in which a correct configuration must be reached eventually, despite all agents starting the execution with arbitrary initial states. In particular, the specification of who is a source and what is its initial input bit may be set by an adversary.We first design a general compiler which can essentially transform any self-stabilizing algorithm with a certain property (called "the bitwise-independence property") that uses -bits messages to one that uses only log -bits messages, while paying only a small penalty in the running time. By applying this compiler recursively we then obtain a self-stabilizing Clock Synchronization protocol, in which agents synchronize their clocks modulo some given integer T , withinÕ(log n log T ) rounds w.h.p., and using messages that contain 3 bits only.We then employ the new Clock Synchronization tool to obtain a self-stabilizing Majority Bit Dissemination protocol which converges inÕ(log n) time, w.h.p., on every initial configuration, provided that the ratio of sources supporting the minority opinion is bounded away from half. Moreover, this protocol also uses only 3 bits per interaction.

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“…One reason is that algorithms in this fault model are very attractive in terms of designing highlyresilient hardware [15]. A substantial amount of work on synchronous counting has been carried out [3,12,16,18,23,29], comprising both positive and negative results.…”

Section: Related Workmentioning

confidence: 99%

“…In addition to the lower bound results, there also exist deterministic algorithms for the synchronous counting problem [12,16,23,29]. Many of these algorithms utilise consensus routines [12,23,29], but obtaining fast and communication-efficient solutions with optimal resilience has been a challenge. For example, Dolev and Hoch [12] apply a pipelining technique,…”

Section: Related Workmentioning

confidence: 99%

“…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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Efficient Counting with Optimal Resilience

Cited by 7 publications

References 30 publications

Self-Stabilising Byzantine Clock Synchronisation Is Almost as Easy as Consensus

Self-Stabilising Byzantine Clock Synchronisation Is Almost as Easy as Consensus

Minimizing message size in stochastic communication patterns: fast self-stabilizing protocols with 3 bits

Near-optimal self-stabilising counting and firing squads

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