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A wait-free queue with polylogarithmic step complexity 步长复杂度为多对数的无等待队列
IF 1.3 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2024-08-17 DOI: 10.1007/s00446-024-00471-7
Hossein Naderibeni, Eric Ruppert

We present a novel linearizable wait-free queue implementation using single-word CAS instructions. Previous lock-free queue implementations from CAS all have amortized step complexity of (Omega (p)) per operation in worst-case executions, where p is the number of processes that access the queue. Our new wait-free queue takes (O(log p)) steps per enqueue and (O(log ^2 p +log q)) steps per dequeue, where q is the size of the queue. A bounded-space version of the implementation has (O(log p log (p+q))) amortized step complexity per operation.

我们提出了一种使用单字 CAS 指令实现的新型可线性化无等待队列。CAS 之前的无锁队列实现在最坏情况下的执行中,每次操作的摊销步骤复杂度都是(Omega (p)),其中 p 是访问队列的进程数。我们的新免等待队列每次enqueue需要(O(log p))步,每次dequeue需要(O(log ^2 p +log q))步,其中q是队列的大小。有界空间版本的实现每次操作的摊销步骤复杂度为(O(log p log (p+q))。
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引用次数: 0
On implementing SWMR registers from SWSR registers in systems with Byzantine failures 在存在拜占庭故障的系统中从 SWSR 寄存器实现 SWMR 寄存器
IF 1.3 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2024-06-06 DOI: 10.1007/s00446-024-00465-5
Xing Hu, Sam Toueg

The implementation of registers from (potentially) weaker registers is a classical problem in the theory of distributed computing. Since Lamport’s pioneering work (Lamport in Distrib Comput 1(2):77–101, 1986), this problem has been extensively studied in the context of asynchronous processes with crash failures. In this paper, we investigate this problem in the context of Byzantine process failures, with and without process signatures. We first prove that, without signatures, there is no wait-free linearizable implementation of a 1-writer n-reader register from atomic 1-writer 1-reader registers. In fact, we show a stronger result, namely, even under the assumption that the writer can only crash and at most one reader can be malicious, there is no linearizable implementation of a 1-writer n-reader register from atomic 1-writer ((n-1))-reader registers that ensures that every correct process eventually completes its operations. In light of this impossibility result, we give two implementations of a 1-writer n-reader register from atomic 1-writer 1-reader registers that work under different assumptions. The first implementation is linearizable (under any combination of Byzantine process failures), but it guarantees that every correct process eventually completes its operations only under the assumption that the writer is correct or no reader is Byzantine—thus matching the impossibility result. The second implementation assumes process signatures; it is wait-free and linearizable under any number and combination of Byzantine process failures.

从(可能)较弱的寄存器实现寄存器是分布式计算理论中的一个经典问题。自 Lamport 的开创性工作(Lamport in Distrib Comput 1(2):77-101,1986)以来,这个问题已在具有崩溃故障的异步进程中得到广泛研究。在本文中,我们将在有进程签名和无进程签名的拜占庭进程故障背景下研究这个问题。我们首先证明,在没有签名的情况下,不存在由原子 1 写 1 读寄存器实现的 1 写 n 读寄存器的无等待线性化实现。事实上,我们证明了一个更强的结果,即即使假设写入器只能崩溃,且最多只有一个读取器可能是恶意的,也不存在由原子1-写入器((n-1))-读取器寄存器组成的1-写入器n-读取器寄存器的可线性化实现,以确保每个正确的进程最终都能完成操作。根据这个不可能结果,我们给出了两个由原子 1 写 1 读寄存器实现的 1 写 n 读寄存器,它们在不同的假设条件下工作。第一种实现是可线性化的(在拜占庭进程失败的任何组合下),但它保证每个正确的进程最终只在写入器正确或没有读取器拜占庭的假设下完成其操作,因此与不可能结果相匹配。第二种实现假定有进程签名;在拜占庭进程失败的任何数量和组合下,它都是无等待和可线性化的。
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引用次数: 0
Developing Irelands first National Student Mental Health and Suicide Prevention Framework for Higher Education. 制定爱尔兰第一个全国高等教育学生心理健康和自杀预防框架。
IF 1.8 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2024-06-01 Epub Date: 2022-04-05 DOI: 10.1017/ipm.2022.10
J Surdey, D Byrne, T Fox

This article focuses on the development of Ireland's first National Student Mental Health and Suicide Prevention Framework for Higher Education. There is growing concern for student mental health in higher education nationally and globally. The majority of students are aged between 18 and 24, which is identified as a high-risk group for mental health difficulties. Recent surveys of student mental illness, mental distress, and low well-being have been recognized by the World Health Organization, the Union of Students in Ireland National Report on Student Mental Health in Third Level Education, the My World survey and the My World 2 study. The Higher Education Authority in Ireland made a commitment to the Department of Health Connecting for Life (Ireland's National Strategy to Reduce Suicide 2015-2020) to form national guidelines for suicide prevention in higher education. In order to deliver on this commitment, The National Student Mental Health and Suicide Prevention Framework was developed. The Framework is informed by international evidence and was the product of a collaborative cross sector and cross disciplinary team including health professionals, government representatives, educators, students, policy makers, community organizations, researchers and clinicians.

本文重点介绍爱尔兰首个全国高等教育学生心理健康和自杀预防框架的发展情况。在全国乃至全球范围内,人们越来越关注高等教育中学生的心理健康问题。大多数学生的年龄在 18-24 岁之间,是心理健康问题的高危人群。世界卫生组织、爱尔兰学生联合会《关于第三级教育中学生心理健康的国家报告》、"我的世界 "调查和 "我的世界 2 "研究都承认最近对学生心理疾病、心理困扰和低幸福感的调查。爱尔兰高等教育管理局向卫生部 "连接生命"(《2015-2020 年爱尔兰减少自杀国家战略》)承诺,将制定在高等教育中预防自杀的国家指导方针。为了兑现这一承诺,爱尔兰制定了《国家学生心理健康与自杀预防框架》。该框架以国际证据为依据,是一个跨部门、跨学科合作团队的成果,其中包括卫生专业人员、政府代表、教育工作者、学生、政策制定者、社区组织、研究人员和临床医生。
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引用次数: 0
Asymmetric distributed trust 非对称分布式信任
IF 1.3 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2024-05-28 DOI: 10.1007/s00446-024-00469-1
Orestis Alpos, Christian Cachin, Björn Tackmann, Luca Zanolini

Quorum systems are a key abstraction in distributed fault-tolerant computing for capturing trust assumptions. They can be found at the core of many algorithms for implementing reliable broadcasts, shared memory, consensus and other problems. This paper introduces asymmetric Byzantine quorum systems that model subjective trust. Every process is free to choose which combinations of other processes it trusts and which ones it considers faulty. Asymmetric quorum systems strictly generalize standard Byzantine quorum systems, which have only one global trust assumption for all processes. This work also presents protocols that implement abstractions of shared memory, broadcast primitives, and a consensus protocol among processes prone to Byzantine faults and asymmetric trust. The model and protocols pave the way for realizing more elaborate algorithms with asymmetric trust.

法定人数系统是分布式容错计算中用于捕捉信任假设的一个关键抽象概念。在许多实现可靠广播、共享内存、共识和其他问题的算法中,它们都是核心。本文介绍了以主观信任为模型的非对称拜占庭法定人数系统。每个进程都可以自由选择信任哪些其他进程的组合,以及认为哪些其他进程有问题。非对称法定人数系统严格概括了标准拜占庭法定人数系统,该系统对所有进程只有一个全局信任假设。这项工作还提出了一些协议,这些协议实现了共享内存的抽象、广播原语以及易发生拜占庭故障和非对称信任的进程之间的共识协议。该模型和协议为实现更复杂的非对称信任算法铺平了道路。
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引用次数: 0
Liveness and latency of Byzantine state-machine replication 拜占庭状态机复制的有效性和延迟
IF 1.3 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2024-05-03 DOI: 10.1007/s00446-024-00466-4
Manuel Bravo, Gregory Chockler, Alexey Gotsman

Byzantine state-machine replication (SMR) ensures the consistency of replicated state in the presence of malicious replicas and lies at the heart of the modern blockchain technology. Byzantine SMR protocols often guarantee safety under all circumstances and liveness only under synchrony. However, guaranteeing liveness even under this assumption is nontrivial. So far we have lacked systematic ways of incorporating liveness mechanisms into Byzantine SMR protocols, which often led to subtle bugs. To close this gap, we introduce a modular framework to facilitate the design of provably live and efficient Byzantine SMR protocols. Our framework relies on a view abstraction generated by a special SMR synchronizer primitive to drive the agreement on command ordering. We present a simple formal specification of an SMR synchronizer and its bounded-space implementation under partial synchrony. We also apply our specification to prove liveness and analyze the latency of three Byzantine SMR protocols via a uniform methodology. In particular, one of these results yields what we believe is the first rigorous liveness proof for the algorithmic core of the seminal PBFT protocol.

拜占庭状态机复制(SMR)可确保在存在恶意复制的情况下复制状态的一致性,是现代区块链技术的核心。拜占庭状态机复制协议通常在所有情况下都能保证安全性,而只有在同步情况下才能保证有效性。然而,即使在这种假设下保证有效性也并非易事。迄今为止,我们还缺乏将有效性机制纳入拜占庭 SMR 协议的系统方法,这往往会导致微妙的错误。为了弥补这一缺陷,我们引入了一个模块化框架,以方便设计可证明有效的拜占庭 SMR 协议。我们的框架依赖于由特殊的 SMR 同步器基元生成的视图抽象来驱动命令排序协议。我们介绍了 SMR 同步器的简单形式规范及其在部分同步下的有界空间实现。我们还应用我们的规范证明了有效性,并通过统一方法分析了三个拜占庭 SMR 协议的延迟。特别是,其中一个结果产生了我们认为是开创性的 PBFT 协议算法核心的第一个严格的有效性证明。
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引用次数: 0
Asynchronous opinion dynamics in social networks 社交网络中的异步舆论动态
IF 1.3 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2024-04-26 DOI: 10.1007/s00446-024-00467-3
Petra Berenbrink, Martin Hoefer, Dominik Kaaser, Pascal Lenzner, Malin Rau, Daniel Schmand

Opinion spreading in a society decides the fate of elections, the success of products, and the impact of political or social movements. A prominent model to study opinion formation processes is due to Hegselmann and Krause. It has the distinguishing feature that stable states do not necessarily show consensus, i.e., the population of agents might not agree on the same opinion. We focus on the social variant of the Hegselmann–Krause model. There are n agents, which are connected by a social network. Their opinions evolve in an iterative, asynchronous process, in which agents are activated one after another at random. When activated, an agent adopts the average of the opinions of its neighbors having a similar opinion (where similarity of opinions is defined using a parameter (varepsilon )). Thus, the set of influencing neighbors of an agent may change over time. We show that such opinion dynamics are guaranteed to converge for any social network. We provide an upper bound of ({text {O}}(n|E|^2 (varepsilon /delta )^2)) on the expected number of opinion updates until convergence to a stable state, where (|E|) is the number of edges of the social network, and (delta ) is a parameter of the stability concept. For the complete social network we show a bound of ({text {O}}(n^3(n^2 + (varepsilon /delta )^2))) that represents a major improvement over the previously best upper bound of ({text {O}}(n^9 (varepsilon /delta )^2)).

社会中的舆论传播决定着选举的命运、产品的成败以及政治或社会运动的影响。Hegselmann 和 Krause 提出了一个研究舆论形成过程的著名模型。该模型的显著特点是,稳定状态并不一定表现出共识,也就是说,群体中的代理人不一定会就同一观点达成一致。我们重点讨论海格塞曼-克劳斯模型的社会变体。有 n 个代理,它们通过一个社会网络连接在一起。它们的观点在一个迭代的、异步的过程中演变,在这个过程中,代理一个接一个地被随机激活。一个代理被激活后,会采纳其具有相似观点的邻居的平均观点(观点的相似性用参数 (varepsilon )来定义)。因此,一个代理的影响邻居集可能会随着时间的推移而改变。我们证明,对于任何社交网络,这种意见动态都能保证收敛。我们为收敛到稳定状态之前的预期意见更新次数提供了一个上限({text {O}}(n|E|^2 (varepsilon /delta )^2)),其中(|E|)是社交网络的边数,(delta )是稳定性概念的参数。对于完整的社交网络,我们展示了一个界限({text {O}}(n^3(n^2+(varepsilon /delta )^2)),这个界限比之前的最佳上限(({text {O}}(n^9 (varepsilon /delta )^2))有了很大的改进。)
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引用次数: 0
Good-case early-stopping latency of synchronous byzantine reliable broadcast: the deterministic case 同步拜占庭可靠广播的良好情况早期停止延迟:确定性案例
IF 1.3 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2024-03-22 DOI: 10.1007/s00446-024-00464-6
Timothé Albouy, Davide Frey, Michel Raynal, François Taïani

This paper considers the good-case latency of Byzantine Reliable Broadcast (BRB), i.e., the time taken by correct processes to deliver a message when the initial sender is correct. This time plays a crucial role in the performance of practical distributed systems. Although significant strides have been made in recent years on this question, progress has mainly focused on either asynchronous or randomized algorithms. By contrast, the good-case latency of deterministic synchronous BRB under a majority of Byzantine faults has been little studied. In particular, it was not known whether a good-case latency below the worst-case bound of (t+1) rounds could be obtained. This work answers this open question positively and proposes a deterministic synchronous Byzantine reliable broadcast that achieves a good-case latency of (textsf{max} (2,t+3-c)) rounds (or equivalently (textsf{max} (2,f+t+3-n))), where t is the upper bound on the number of Byzantine processes, (fle t) the number of effectively Byzantine processes, and (c=n-f) the number of effectively correct processes. The proposed algorithm does not put any constraint on t, and assumes an authenticated setting, in which individual processes can sign the messages they send, and verify the authenticity of the signatures they receive.

本文考虑了拜占庭可靠广播(Byzantine Reliable Broadcast,BRB)的良好情况延迟,即当初始发送者正确时,正确进程传递信息所需的时间。这段时间对实际分布式系统的性能起着至关重要的作用。虽然近年来在这一问题上取得了长足进步,但进展主要集中在异步或随机算法上。相比之下,人们对大多数拜占庭故障下确定性同步 BRB 的良好情况延迟时间研究甚少。尤其是,人们还不知道能否获得低于最坏情况下的(t+1)轮的良好情况下的延迟。这项工作正面回答了这个开放性问题,并提出了一种确定性同步拜占庭可靠广播,它能实现 (textsf{max} (2,t+3-c)) 轮的良好情况下的延迟(或等价于 (textsf{max} (2、t+3-n)),其中 t 是拜占庭进程数量的上限,(fle t )是有效拜占庭进程的数量,(c=n-f )是有效正确进程的数量。所提出的算法对 t 不做任何限制,并假定了一个经过验证的环境,在这个环境中,各个进程可以对它们发送的信息进行签名,并验证它们收到的签名的真实性。
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引用次数: 0
Early adapting to trends: self-stabilizing information spread using passive communication 提前适应趋势:利用被动传播实现信息传播的自我稳定
IF 1.3 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2024-02-22 DOI: 10.1007/s00446-024-00462-8
Amos Korman, Robin Vacus

How to efficiently and reliably spread information in a system is one of the most fundamental problems in distributed computing. Recently, inspired by biological scenarios, several works focused on identifying the minimal communication resources necessary to spread information under faulty conditions. Here we study the self-stabilizing bit-dissemination problem, introduced by Boczkowski, Korman, and Natale in [SODA 2017]. The problem considers a fully-connected network of n agents, with a binary world of opinions, one of which is called correct. At any given time, each agent holds an opinion bit as its public output. The population contains a source agent which knows which opinion is correct. This agent adopts the correct opinion and remains with it throughout the execution. We consider the basic (mathcal {PULL}) model of communication, in which each agent observes relatively few randomly chosen agents in each round. The goal of the non-source agents is to quickly converge on the correct opinion, despite having an arbitrary initial configuration, i.e., in a self-stabilizing manner. Once the population converges on the correct opinion, it should remain with it forever. Motivated by biological scenarios in which animals observe and react to the behavior of others, we focus on the extremely constrained model of passive communication, which assumes that when observing another agent the only information that can be extracted is the opinion bit of that agent. We prove that this problem can be solved in a poly-logarithmic in n number of rounds with high probability, while sampling a logarithmic number of agents at each round. Previous works solved this problem faster and using fewer samples, but they did that by decoupling the messages sent by agents from their output opinion, and hence do not fit the framework of passive communication. Moreover, these works use complex recursive algorithms with refined clocks that are unlikely to be used by biological entities. In contrast, our proposed algorithm has a natural appeal as it is based on letting agents estimate the current tendency direction of the dynamics, and then adapt to the emerging trend.

如何在系统中高效可靠地传播信息是分布式计算中最基本的问题之一。最近,受生物场景的启发,有几项研究集中于确定在故障条件下传播信息所需的最小通信资源。在此,我们研究 Boczkowski、Korman 和 Natale 在 [SODA 2017] 中提出的自稳定比特传播问题。该问题考虑了一个由 n 个代理组成的全连接网络,该网络具有二元意见世界,其中一种意见被称为正确意见。在任何给定时间,每个代理都持有一个意见位作为其公共输出。群体中包含一个源代理,它知道哪种观点是正确的。该代理采用正确的观点,并在整个执行过程中保持不变。我们考虑基本的通信模型,即每个代理在每一轮中观察相对较少的随机选择的代理。非源代理的目标是,尽管有一个任意的初始配置,也就是以自稳定的方式,快速收敛到正确的意见上。一旦群体趋同于正确的观点,就应该永远保持下去。受动物观察并对他人行为做出反应的生物场景的启发,我们重点研究了极其受限的被动交流模型,该模型假定当观察另一个代理时,唯一能提取的信息就是该代理的意见位。我们证明,这个问题可以在 n 个回合内以高概率的多对数方式解决,同时在每个回合中对数数量的代理进行采样。以前的研究能以更快的速度和更少的样本解决这个问题,但它们是通过将代理发送的信息与其输出意见解耦来实现的,因此不符合被动通信的框架。此外,这些研究还使用了复杂的递归算法和精制时钟,而生物实体不太可能使用这些算法。相比之下,我们提出的算法则具有天然的吸引力,因为它是基于让代理估计当前的动态趋势方向,然后适应新出现的趋势。
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引用次数: 0
Component stability in low-space massively parallel computation 低空间大规模并行计算中的组件稳定性
IF 1.3 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2024-02-08 DOI: 10.1007/s00446-024-00461-9
Artur Czumaj, Peter Davies-Peck, Merav Parter

In this paper, we study the power and limitations of component-stable algorithms in the low-space model of massively parallel computation (MPC). Recently Ghaffari, Kuhn and Uitto (FOCS 2019) introduced the class of component-stable low-space MPC algorithms, which are, informally, those algorithms for which the outputs reported by the nodes in different connected components are required to be independent. This very natural notion was introduced to capture most (if not all) of the known efficient MPC algorithms to date, and it was the first general class of MPC algorithms for which one can show non-trivial conditional lower bounds. In this paper we enhance the framework of component-stable algorithms and investigate its effect on the complexity of randomized and deterministic low-space MPC. Our key contributions include: 1. We revise and formalize the lifting approach of Ghaffari, Kuhn and Uitto. This requires a very delicate amendment of the notion of component stability, which allows us to fill in gaps in the earlier arguments. 2. We also extend the framework to obtain conditional lower bounds for deterministic algorithms and fine-grained lower bounds that depend on the maximum degree (Delta ). 3. We demonstrate a collection of natural graph problems for which deterministic component-unstable algorithms break the conditional lower bound obtained for component-stable algorithms. This implies that, in the context of deterministic algorithms, component-stable algorithms are conditionally weaker than the component-unstable ones. 4. We also show that the restriction to component-stable algorithms has an impact in the randomized setting. We present a natural problem which can be solved in O(1) rounds by a component-unstable MPC algorithm, but requires (Omega (log log ^* n)) rounds for any component-stable algorithm, conditioned on the connectivity conjecture. Altogether our results imply that component-stability might limit the computational power of the low-space MPC model, at least in certain contexts, paving the way for improved upper bounds that escape the conditional lower bound setting of Ghaffari, Kuhn, and Uitto.

本文将研究大规模并行计算(MPC)低空间模型中组件稳定算法的威力和局限性。最近,Ghaffari、Kuhn 和 Uitto(FOCS 2019)提出了一类组件稳定的低空间 MPC 算法,非正式地说,这些算法要求不同连接组件中的节点报告的输出是独立的。引入这一非常自然的概念,可以捕捉到迄今为止已知的大多数(如果不是全部)高效 MPC 算法,而且这是第一类可以证明非难条件下界的 MPC 算法。在本文中,我们增强了组件稳定算法的框架,并研究了它对随机和确定性低空间 MPC 复杂性的影响。我们的主要贡献包括1.我们修改并正式确定了 Ghaffari、Kuhn 和 Uitto 的提升方法。这需要对组件稳定性的概念进行非常微妙的修正,从而使我们能够填补早期论证中的空白。2.2. 我们还扩展了框架,以获得确定性算法的条件下界和取决于最大度 (Delta )的细粒度下界。3.我们展示了一系列自然图问题,对于这些问题,确定性成分不稳定算法打破了成分稳定算法的条件下界。这意味着,在确定性算法中,成分稳定算法在条件上弱于成分不稳定算法。4.4. 我们还证明,对组件稳定算法的限制对随机化环境也有影响。我们提出了一个自然问题,该问题可以用组件不稳定的 MPC 算法在 O(1) 轮内解决,但对于任何组件稳定的算法,在连通性猜想的条件下,需要 (ω (log log ^* n)) 轮。总之,我们的结果意味着,至少在某些情况下,组件稳定性可能会限制低空间 MPC 模型的计算能力,从而为摆脱加法里、库恩和乌伊托的条件下限设置的改进上界铺平了道路。
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引用次数: 0
Distributed computing with the cloud 云计算的分布式计算
IF 1.3 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2024-02-01 DOI: 10.1007/s00446-024-00460-w
Yehuda Afek, Gal Giladi, Boaz Patt-Shamir

We investigate the effect of omnipresent cloud storage on distributed computing. To this end, we specify a network model with links of prescribed bandwidth that connect standard processing nodes, and, in addition, passive storage nodes. Each passive node represents a cloud storage system, such as Dropbox, Google Drive etc. We study a few tasks in this model, assuming a single cloud node connected to all other nodes, which are connected to each other arbitrarily. We give implementations for basic tasks of collaboratively writing to and reading from the cloud, and for more advanced applications such as matrix multiplication and federated learning. Our results show that utilizing node-cloud links as well as node-node links can considerably speed up computations, compared to the case where processors communicate either only through the cloud or only through the network links. We first show how to optimally read and write large files to and from the cloud in general graphs using flow techniques. We use these primitives to derive algorithms for combining, where every processor node has an input value and the task is to compute a combined value under some given associative operator. In the special but common case of “fat links,” where we assume that links between processors are bidirectional and have high bandwidth, we provide near-optimal algorithms for any commutative combining operator (such as vector addition). For the task of matrix multiplication (or other non-commutative combining operators), where the inputs are ordered, we present tight results in the simple “wheel” network, where procesing nodes are arranged in a ring, and are all connected to a single cloud node.

我们研究了无所不在的云存储对分布式计算的影响。为此,我们指定了一个网络模型,该模型具有连接标准处理节点和被动存储节点的规定带宽链路。每个被动节点代表一个云存储系统,如 Dropbox、Google Drive 等。我们研究了该模型中的一些任务,假设一个云节点与所有其他节点相连,而这些节点之间的连接是任意的。我们给出了向云协作写入和从云协作读取的基本任务以及矩阵乘法和联合学习等更高级应用的实现方法。我们的结果表明,与处理器仅通过云或仅通过网络链接进行通信的情况相比,利用节点-云链接以及节点-节点链接可以大大加快计算速度。我们首先展示了如何利用流技术在一般图中以最佳方式读写云中的大文件。在这种情况下,每个处理器节点都有一个输入值,任务是根据给定的关联算子计算一个组合值。在 "胖链接 "这种特殊但常见的情况下,我们假定处理器之间的链接是双向的,并且具有很高的带宽,因此我们为任何交换组合算子(如向量加法)提供了近乎最优的算法。对于输入有序的矩阵乘法(或其他非交换组合运算)任务,我们在简单的 "轮子 "网络中给出了严密的结果,在该网络中,处理节点排列成环形,并全部连接到一个云节点。
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引用次数: 0
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Distributed Computing
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