Making asynchronous distributed computations robust to noise

Censor-Hillel, Keren; Gelles, Ran; Haeupler, Bernhard

doi:10.1007/s00446-018-0343-5

Cited by 15 publications

(6 citation statements)

References 40 publications

(41 reference statements)

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“…Hoza and Schulman [HS16] showed a general compiler for synchronous distributed algorithms that handles an adversarial error rate of O(1/|E|) while incurring a constant communication overhead. [CHGH18] extended this result for the asynchronous setting, see [Gel17] for additional error models in interactive coding.…”

Section: Distributed Compiler For Resilient Computationmentioning

confidence: 96%

Low Congestion Cycle Covers and Their Applications

Parter¹,

Yogev²

2019

Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms

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A cycle cover of a bridgeless graph G is a collection of simple cycles in G such that each edge e appears on at least one cycle. The common objective in cycle cover computation is to minimize the total lengths of all cycles. Motivated by applications to distributed computation, we introduce the notion of low-congestion cycle covers, in which all cycles in the cycle collection are both short and nearly edge-disjoint. Formally, a (d, c)-cycle cover of a graph G is a collection of cycles in G in which each cycle is of length at most d and each edge participates in at least one cycle and at most c cycles.A-priori, it is not clear that cycle covers that enjoy both a small overlap and a short cycle length even exist, nor if it is possible to efficiently find them. Perhaps quite surprisingly, we prove the following: Every bridgeless graph of diameter D admits a (d, c)-cycle cover where d =Õ(D) and c =Õ(1). That is, the edges of G can be covered by cycles such that each cycle is of length at most O(D) and each edge participates in at most O(1) cycles. These parameters are existentially tight up to polylogarithmic terms.Furthermore, we show how to extend our result to achieve universally optimal cycle covers. Let C e is the length of the shortest cycle that covers e, and let OPT(G) = max e∈G C e . We show that every bridgeless graph admits a (d, c)-cycle cover where d =Õ(OPT(G)) and c =Õ(1).We demonstrate the usefulness of low congestion cycle covers in different settings of resilient computation. For instance, we consider a Byzantine fault model where in each round, the adversary chooses a single message and corrupt in an arbitrarily manner. We provide a compiler that turns any r-round distributed algorithm for a graph G with diameter D, into an equivalent fault tolerant algorithm with r · poly(D) rounds.Theorem 2 (Optimal Cycle Cover, Informal). There exists a construction of (nearly) universally optimal (d, c)-cycle covers with d = O(OPT(G)) and c = O(1), where OPT(G) is the best possible cycle length (i.e., even without the congestion constraint).In fact, our algorithm can be made nearly optimal with respect to each individual edge. That is, we can construct a cycle cover that covers each edge e by a cycle whose length is O(|C e |) where C e is the shortest cycle in G that goes through e. The congestion for any edge remains O(1).Turning to the distributed setting, we also provide a construction of cycle covers for the family of minor-closed graphs. Our construction is (nearly) optimal in terms of both its run-time and in the parameters of the cycle cover. Minor-closed graphs have recently attracted a lot of attention in the setting of distributed network optimization [GH16, HIZ16a, GP17, HLZ18, LMR18].Theorem 3 (Optimal Cycle Cover Construction for Minor Close Graphs, Informal). For the family of minor closed graphs, there exists an O(OPT(G))-round algorithm that constructs (d, c)-cycle cover with d = O(OPT(G)), c = O(1), where OPT(G) is equal to the best possible cycle length (i.e., even without the constraint on the...

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Section: Distributed Compiler For Resilient Computationmentioning

confidence: 96%

Low Congestion Cycle Covers and Their Applications

Parter¹,

Yogev²

2019

Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms

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“…Censor-Hillel, Gelles, and Haeupler [CGH18] constructed asynchronous schemes, where the parties do not know the topology of the network (an assumption that is very common in the distributed computation community). Their scheme is resilient to O(1/n) noise and has a rate of 1/O(n log 2 n).…”

Section: Related Workmentioning

confidence: 99%

Efficient Multiparty Interactive Coding for Insertions, Deletions, and Substitutions

Gelles

Kalai

Ramnarayan

2019

Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing

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In the field of interactive coding, two or more parties wish to carry out a distributed computation over a communication network that may be noisy. The ultimate goal is to develop efficient coding schemes that can tolerate a high level of noise while increasing the communication by only a constant factor (i.e., constant rate).In this work we consider synchronous communication networks over an arbitrary topology, in the powerful adversarial insertion-deletion noise model. Namely, the noisy channel may adversarially alter the content of any transmitted symbol, as well as completely remove a transmitted symbol or inject a new symbol into the channel.We provide efficient, constant rate schemes that successfully conduct any computation with high probability as long as the adversary corrupts at most ε m fraction of the total communication, where m is the number of links in the network and ε is a small constant. This scheme assumes the parties share a random string to which the adversarial noise is oblivious. We can remove this assumption at the price of being resilient to ε m log m adversarial error. While previous work considered the insertion-deletion noise model in the two-party setting, to the best of our knowledge, our scheme is the first multiparty scheme that is resilient to insertions and deletions. Furthermore, our scheme is the first computationally efficient scheme in the multiparty setting that is resilient to adversarial noise.1 By "arbitrary" we mean that the topology of the network can be an arbitrary graph G = (V, E) where each node is a party and each edge is a communication channel connecting the parties associated with these nodes.2 That is, a channel that flips every bit with some constant probability ε ∈ (0, 1/2). 3 [JKL15] obtained this result for the specific star network, whereas [HS16] generalized this result to a network with arbitrary topology. 4 We assume that each insertion, deletion, or substitution counts as a single corruption.Theorem 1.2 (no common randomness, non-oblivious noise, informal). Let G = (V, E) be an arbitrary synchronous network with n = |V | nodes and m = |E| links. For any noiseless protocol Π over G with a predetermined order of speaking, and for any sufficiently small constant ε, there exists an efficient coding scheme that simulates Π over a noisy network G. The simulated protocol is robust to adversarial insertion, deletion, and substituition noise, assuming at most (ε/m log m)-fraction of the communication is corrupted. The simulated protocol communicates O(CC(Π)) bits, and succeeds with probability at least 1 − exp(−CC(Π)/m).In Appendix B we consider the case where the adversarial channel is non-oblivious, however, the parties pre-share randomness. In this case we show a coding scheme (Algorithm C) that is resilient to a somewhat higher noise level of ε/m log log m-fraction of insertion and deletion noise, while still incurring a constant blowup in the communication. See Appendix B for the complete details.3 Lemma 6.3. Let |Π| = CC(Π) 5m log(m) and let ε > 0 be a su...

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“…In Subsection 1.3 we introduced and motivated the noisy communication model studied in [16,38,39] and adopted in this paper. Another model of noisy communication for distributed systems is the one considered in [3,19]. Departing significantly from the model we adopt in this paper, here there is a (worst-case) adversary that can adaptively flip the bits exchanged during the execution of any protocol and the goal is to provide a robust version of the protocol under the assumption that the adversary has a limited budget on the number of bits it can change.…”

Section: Noiseless Communicationmentioning

confidence: 99%

“…Departing significantly from the model we adopt in this paper, here there is a (worst-case) adversary that can adaptively flip the bits exchanged during the execution of any protocol and the goal is to provide a robust version of the protocol under the assumption that the adversary has a limited budget on the number of bits it can change. Efficient solutions for such models typically use silent rounds [3] and error-correcting codes [3,19]. In [37] a different task is studied in a model with noisy interactions: all n nodes of a network hold a bit and they wish to transmit to a single receiver.…”

Section: Noiseless Communicationmentioning

confidence: 99%

Consensus Needs Broadcast in Noiseless Models but can be Exponentially Easier in the Presence of Noise

Clementi,

Gualà,

Natale

et al. 2018

Preprint

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Consensus and Broadcast are two fundamental problems in distributed computing, whose solutions have several applications. Intuitively, Consensus should be no harder than Broadcast, and this can be rigorously established in several models. Can Consensus be easier than Broadcast?In models that allow noiseless communication, we prove a reduction of (a suitable variant of) Broadcast to binary Consensus, that preserves the communication model and all complexity parameters such as randomness, number of rounds, communication per round, etc., while there is a loss in the success probability of the protocol. Using this reduction, we get, among other applications, the first logarithmic lower bound on the number of rounds needed to achieve Consensus in the uniform GOSSIP model on the complete graph. The lower bound is tight and, in this model, Consensus and Broadcast are equivalent.We then turn to distributed models with noisy communication channels that have been studied in the context of some bio-inspired systems. In such models, only one noisy bit is exchanged when a communication channel is established between two nodes, and so one cannot easily simulate a noiseless protocol by using error-correcting codes. An Ω(ε −2 n) lower bound on the number of rounds needed for Broadcast is proved by Boczkowski et al. [PLOS Comp. Bio. 2018] in one such model (noisy uniform PULL, where ε is a parameter that measures the amount of noise). In such model, we prove a new Θ(ε −2 n log n) bound for Broadcast and a Θ(ε −2 log n) bound for binary Consensus, thus establishing an exponential gap between the number of rounds necessary for Consensus versus Broadcast.

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Making asynchronous distributed computations robust to noise

Cited by 15 publications

References 40 publications

Low Congestion Cycle Covers and Their Applications

Low Congestion Cycle Covers and Their Applications

Efficient Multiparty Interactive Coding for Insertions, Deletions, and Substitutions

Consensus Needs Broadcast in Noiseless Models but can be Exponentially Easier in the Presence of Noise

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