Distributed Computing最新文献

{"title":"Iterative approximate Byzantine consensus in arbitrary directed graphs","authors":"Lewis Tseng, Guanfeng Liang, Nitin H. Vaidya","doi":"10.1007/s00446-024-00468-2","DOIUrl":"https://doi.org/10.1007/s00446-024-00468-2","url":null,"abstract":"<p>This paper identifies necessary and sufficient conditions for the existence of <i>iterative</i> algorithms that achieve <i>approximate Byzantine consensus</i> in arbitrary directed graphs, where each directed link represents a communication channel between a pair of nodes. The class of iterative algorithms considered in this paper ensures that, after each iteration of the algorithm, the state of each fault-free node remains in the <i>convex hull</i> of the states of the fault-free nodes at the end of the previous iteration. We present the necessary and sufficient condition for the existence of such iterative consensus algorithms in synchronous <i>arbitrary</i> point-to-point networks in presence of <i>Byzantine faults</i> in two different equivalent forms. We prove the necessity using an indistinguishability argument. For sufficiency, we develop a proof framework, which first uses a series of “transition matrices” to model the state evolution of the fault-free nodes using our algorithm, and then proves the correctness by identifying important properties of the matrices. The proof framework is useful for other iterative fault-tolerant algorithms. We discuss the extensions to asynchronous systems and the Byzantine links fault model.</p>","PeriodicalId":50569,"journal":{"name":"Distributed Computing","volume":"28 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153650","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Liveness and latency of Byzantine state-machine replication","authors":"Manuel Bravo, Gregory Chockler, Alexey Gotsman","doi":"10.1007/s00446-024-00466-4","DOIUrl":"https://doi.org/10.1007/s00446-024-00466-4","url":null,"abstract":"<p>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 <i>view</i> abstraction generated by a special <i>SMR synchronizer</i> 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.\u0000</p>","PeriodicalId":50569,"journal":{"name":"Distributed Computing","volume":"17 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140886522","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Asynchronous opinion dynamics in social networks","authors":"Petra Berenbrink, Martin Hoefer, Dominik Kaaser, Pascal Lenzner, Malin Rau, Daniel Schmand","doi":"10.1007/s00446-024-00467-3","DOIUrl":"https://doi.org/10.1007/s00446-024-00467-3","url":null,"abstract":"<p>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 <i>n</i> 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 <span>(varepsilon )</span>). 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 <span>({text {O}}(n|E|^2 (varepsilon /delta )^2))</span> on the expected number of opinion updates until convergence to a stable state, where <span>(|E|)</span> is the number of edges of the social network, and <span>(delta )</span> is a parameter of the stability concept. For the complete social network we show a bound of <span>({text {O}}(n^3(n^2 + (varepsilon /delta )^2)))</span> that represents a major improvement over the previously best upper bound of <span>({text {O}}(n^9 (varepsilon /delta )^2))</span>.</p>","PeriodicalId":50569,"journal":{"name":"Distributed Computing","volume":"27 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140806115","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the power of bounded asynchrony: convergence by autonomous robots with limited visibility","authors":"David Kirkpatrick, Irina Kostitsyna, Alfredo Navarra, Giuseppe Prencipe, Nicola Santoro","doi":"10.1007/s00446-024-00463-7","DOIUrl":"https://doi.org/10.1007/s00446-024-00463-7","url":null,"abstract":"<p>A distributed algorithm <span>({mathcal {A}})</span> solves the <span>Point Convergence</span> task if an arbitrarily large collection of entities, starting in an arbitrary configuration, move under the control of <span>({mathcal {A}})</span> to eventually form and thereafter maintain configurations in which the separation between all entities is arbitrarily small. This fundamental task in the standard <span>(mathcal {OBLOT})</span> model of autonomous mobile entities has been previously studied in a variety of settings, including full visibility, exact measurements (including distances and angles), and synchronous activation of entities. Our study concerns the minimal assumptions under which entities, moving asynchronously with limited and unknown visibility range and subject to limited imprecision in measurements, can be guaranteed to converge in this way. We present an algorithm operating under these constraints that solves <span>Point Convergence</span>, for entities moving in two or three dimensional space, with any bounded degree of asynchrony. We also prove that under similar realistic constraints, but unbounded asynchrony, <span>Point Convergence</span> in the plane is not possible in general, contingent on the natural assumption that algorithms maintain the (visible) connectivity among entities present in the initial configuration. This variant, that we call <span>Cohesive Convergence</span>, serves to distinguish the power of bounded and unbounded asynchrony in the control of autonomous mobile entities, settling a long-standing question whether in the Euclidean plane synchronously scheduled entities are more powerful than asynchronously scheduled entities.</p>","PeriodicalId":50569,"journal":{"name":"Distributed Computing","volume":"2675 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140590209","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Good-case early-stopping latency of synchronous byzantine reliable broadcast: the deterministic case","authors":"Timothé Albouy, Davide Frey, Michel Raynal, François Taïani","doi":"10.1007/s00446-024-00464-6","DOIUrl":"https://doi.org/10.1007/s00446-024-00464-6","url":null,"abstract":"<p>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 <span>(t+1)</span> 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 <span>(textsf{max} (2,t+3-c))</span> rounds (or equivalently <span>(textsf{max} (2,f+t+3-n))</span>), where <i>t</i> is the upper bound on the number of Byzantine processes, <span>(fle t)</span> the number of effectively Byzantine processes, and <span>(c=n-f)</span> the number of effectively correct processes. The proposed algorithm does not put any constraint on <i>t</i>, and assumes an authenticated setting, in which individual processes can sign the messages they send, and verify the authenticity of the signatures they receive.</p>","PeriodicalId":50569,"journal":{"name":"Distributed Computing","volume":"1 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140204000","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Early adapting to trends: self-stabilizing information spread using passive communication","authors":"Amos Korman, Robin Vacus","doi":"10.1007/s00446-024-00462-8","DOIUrl":"https://doi.org/10.1007/s00446-024-00462-8","url":null,"abstract":"<p>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 <i>bit-dissemination</i> problem, introduced by Boczkowski, Korman, and Natale in [SODA 2017]. The problem considers a fully-connected network of <i>n</i> <i>agents</i>, with a binary world of <i>opinions</i>, one of which is called <i>correct</i>. At any given time, each agent holds an opinion bit as its public output. The population contains a <i>source</i> agent which knows which opinion is correct. This agent adopts the correct opinion and remains with it throughout the execution. We consider the basic <span>(mathcal {PULL})</span> 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 <i>passive communication</i>, 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 <i>n</i> 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.</p>","PeriodicalId":50569,"journal":{"name":"Distributed Computing","volume":"85 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139945961","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Component stability in low-space massively parallel computation","authors":"Artur Czumaj, Peter Davies-Peck, Merav Parter","doi":"10.1007/s00446-024-00461-9","DOIUrl":"https://doi.org/10.1007/s00446-024-00461-9","url":null,"abstract":"<p>In this paper, we study the power and limitations of component-stable algorithms in the low-space model of <i>massively parallel computation (</i><span>MPC</span><i>)</i>. Recently Ghaffari, Kuhn and Uitto (FOCS 2019) introduced the class of <i>component-stable</i> low-space <span>MPC</span> 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 <span>MPC</span> algorithms to date, and it was the first general class of <span>MPC</span> 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 <span>MPC</span>. 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 <span>(Delta )</span>. 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 <i>O</i>(1) rounds by a component-unstable <span>MPC</span> algorithm, but requires <span>(Omega (log log ^* n))</span> 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 <span>MPC</span> 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.\u0000</p>","PeriodicalId":50569,"journal":{"name":"Distributed Computing","volume":"13 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139765601","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Distributed computing with the cloud","authors":"Yehuda Afek, Gal Giladi, Boaz Patt-Shamir","doi":"10.1007/s00446-024-00460-w","DOIUrl":"https://doi.org/10.1007/s00446-024-00460-w","url":null,"abstract":"<p>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 <i>combining</i>, 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.</p>","PeriodicalId":50569,"journal":{"name":"Distributed Computing","volume":"61 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139666685","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Expected linear round synchronization: the missing link for linear Byzantine SMR","authors":"Oded Naor, Idit Keidar","doi":"10.1007/s00446-023-00459-9","DOIUrl":"https://doi.org/10.1007/s00446-023-00459-9","url":null,"abstract":"<p>State Machine Replication (SMR) solutions often divide time into rounds, with a designated leader driving decisions in each round. Progress is guaranteed once all correct processes <i>synchronize</i> to the same round, and the leader of that round is correct. Recently suggested Byzantine SMR solutions such as HotStuff, and LibraBFT achieve progress with a linear message complexity and a constant time complexity once such round synchronization occurs. But round synchronization itself incurs an additional cost. By Dolev and Reischuk’s lower bound, any deterministic solution must have <span>(Omega (n^2))</span> communication complexity. Yet the question of randomized round synchronization with an expected linear message complexity remained open. We present an algorithm that, for the first time, achieves round synchronization with expected linear message complexity and expected constant latency. Existing protocols can use our round synchronization algorithm to solve Byzantine SMR with the same asymptotic performance.\u0000</p>","PeriodicalId":50569,"journal":{"name":"Distributed Computing","volume":"256 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139410118","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Byzantine consensus is $$Theta (n^2)$$ : the Dolev-Reischuk bound is tight even in partial synchrony!","authors":"Pierre Civit, Muhammad Ayaz Dzulfikar, Seth Gilbert, Vincent Gramoli, Rachid Guerraoui, Jovan Komatovic, Manuel Vidigueira","doi":"10.1007/s00446-023-00458-w","DOIUrl":"https://doi.org/10.1007/s00446-023-00458-w","url":null,"abstract":"<p>The Dolev-Reischuk bound says that any deterministic Byzantine consensus protocol has (at least) quadratic (in the number of processes) communication complexity in the worst case: given a system with <i>n</i> processes and at most <span>(f &lt; n / 3)</span> failures, any solution to Byzantine consensus exchanges <span>(Omega big (n^2big ))</span> words, where a word contains a constant number of values and signatures. While it has been shown that the bound is tight in synchronous environments, it is still unknown whether a consensus protocol with quadratic communication complexity can be obtained in partial synchrony where the network alternates between (1) asynchronous periods, with unbounded message delays, and (2) synchronous periods, with <span>(delta )</span>-bounded message delays. Until now, the most efficient known solutions for Byzantine consensus in partially synchronous settings had cubic communication complexity (e.g., HotStuff, binary DBFT). This paper closes the existing gap by introducing <span>SQuad</span>, a partially synchronous Byzantine consensus protocol with <span>(Obig (n^2big ))</span> worst-case communication complexity. In addition, <span>SQuad</span> is optimally-resilient (tolerating up to <span>(f &lt; n / 3)</span> failures) and achieves <span>(O(f cdot delta ))</span> worst-case latency complexity. The key technical contribution underlying <span>SQuad</span> lies in the way we solve <i>view synchronization</i>, the problem of bringing all correct processes to the same view with a correct leader for sufficiently long. Concretely, we present <span>RareSync</span>, a view synchronization protocol with <span>(Obig (n^2big ))</span> communication complexity and <span>(O(f cdot delta ))</span> latency complexity, which we utilize in order to obtain <span>SQuad</span>.</p>","PeriodicalId":50569,"journal":{"name":"Distributed Computing","volume":"30 26 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138574723","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}