This paper proposes a simple topological characterization of a large class of fair adversarial models via affine tasks: sub-complexes of the second iteration of the standard chromatic subdivision. We show that the task computability of a model in the class is precisely captured by iterations of the corresponding affine task. Fair adversaries include, but are not restricted to, the models of wait-freedom, t-resilience, and k-concurrency. Our results generalize and improve all previously derived topological characterizations of the ability of a model to solve distributed tasks.
{"title":"An Asynchronous Computability Theorem for Fair Adversaries","authors":"P. Kuznetsov, Thibault Rieutord, Yuan He","doi":"10.1145/3212734.3212765","DOIUrl":"https://doi.org/10.1145/3212734.3212765","url":null,"abstract":"This paper proposes a simple topological characterization of a large class of fair adversarial models via affine tasks: sub-complexes of the second iteration of the standard chromatic subdivision. We show that the task computability of a model in the class is precisely captured by iterations of the corresponding affine task. Fair adversaries include, but are not restricted to, the models of wait-freedom, t-resilience, and k-concurrency. Our results generalize and improve all previously derived topological characterizations of the ability of a model to solve distributed tasks.","PeriodicalId":198284,"journal":{"name":"Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128192744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The notion of summarization is to provide a compact representation of data which approximately captures its essential characteristics. If such summaries can be created, they can lead to efficient distributed algorithms which exchange summaries in order to compute a desired function. In this talk, I'll describe recent efforts in this direction for problems inspired by machine learning: building graphical models over evolving, distributed training examples, and solving robust regression problems over large, distributed data sets.
{"title":"Data Summarization and Distributed Computation","authors":"Graham Cormode","doi":"10.1145/3212734.3212795","DOIUrl":"https://doi.org/10.1145/3212734.3212795","url":null,"abstract":"The notion of summarization is to provide a compact representation of data which approximately captures its essential characteristics. If such summaries can be created, they can lead to efficient distributed algorithms which exchange summaries in order to compute a desired function. In this talk, I'll describe recent efforts in this direction for problems inspired by machine learning: building graphical models over evolving, distributed training examples, and solving robust regression problems over large, distributed data sets.","PeriodicalId":198284,"journal":{"name":"Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132828412","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the minimum k-edge-connected spanning subgraph (k-ECSS) problem the goal is to find the minimum weight subgraph resistant to up to k-1 edge failures. This is a central problem in network design, and a natural generalization of the minimum spanning tree (MST) problem. While the MST problem has been studied extensively by the distributed computing community, for k ≥2 less is known in the distributed setting. In this paper, we present fast randomized distributed approximation algorithms for k-ECSS in the CONGEST model. Our first contribution is an Õ (D + √ )-round O(logn )-approximation for 2-ECSS, for a graph with n vertices and diameter D. The time complexity of our algorithm is almost tight and almost matches the time complexity of the MST problem. For larger constant values of k we give an Õ (n) -round O(logn ) -approximation. Additionally, in the special case of unweighted 3-ECSS we show how to improve the time complexity to O(D log^3n ) rounds. All our results significantly improve the time complexity of previous algorithms.
{"title":"Distributed Approximation of Minimum k-edge-connected Spanning Subgraphs","authors":"Michal Dory","doi":"10.1145/3212734.3212760","DOIUrl":"https://doi.org/10.1145/3212734.3212760","url":null,"abstract":"In the minimum k-edge-connected spanning subgraph (k-ECSS) problem the goal is to find the minimum weight subgraph resistant to up to k-1 edge failures. This is a central problem in network design, and a natural generalization of the minimum spanning tree (MST) problem. While the MST problem has been studied extensively by the distributed computing community, for k ≥2 less is known in the distributed setting. In this paper, we present fast randomized distributed approximation algorithms for k-ECSS in the CONGEST model. Our first contribution is an Õ (D + √ )-round O(logn )-approximation for 2-ECSS, for a graph with n vertices and diameter D. The time complexity of our algorithm is almost tight and almost matches the time complexity of the MST problem. For larger constant values of k we give an Õ (n) -round O(logn ) -approximation. Additionally, in the special case of unweighted 3-ECSS we show how to improve the time complexity to O(D log^3n ) rounds. All our results significantly improve the time complexity of previous algorithms.","PeriodicalId":198284,"journal":{"name":"Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124377207","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study a game theoretic model where a coalition of processors might collude to bias the outcome of the protocol, where we assume that the processors always prefer any legitimate outcome over a non-legitimate one. We show that the problems of Fair Leader Election and Fair Coin Toss are equivalent, and focus on Fair Leader Election. Our main focus is on a directed asynchronous ring of n processors, where we investigate the protocol proposed by Abraham et al. [4] and studied in Afek et al. [5]. We show that in general the protocol is resilient only to sub-linear size coalitions. Specifically, we show that Ω( p n logn) randomly located processors or Ω( 3 √ n) adversarially located processors can force any outcome. We complement this by showing that the protocol is resilient to any adversarial coalition of size O( 4 √ n). We propose a modification to the protocol, and show that it is resilient to every coalition of size ?( √ n), by exhibiting both an attack and a resilience result. For every k ≥ 1, we define a family of graphs Gk that can be simulated by trees where each node in the tree simulates at most k processors. We show that for every graph in Gk , there is no fair leader election protocol that is resilient to coalitions of size k. Our result generalizes a previous result of Abraham et al. [4] that states that for every graph, there is no fair leader election protocol which is resilient to coalitions of size ?n/2 ?.
我们研究了一个博弈论模型，其中一个处理器联盟可能串通起来对协议的结果产生偏见，其中我们假设处理器总是更喜欢任何合法的结果而不是不合法的结果。我们证明公平领袖选举问题和公平抛硬币问题是等价的，并重点讨论公平领袖选举问题。我们主要关注的是n个处理器的定向异步环，我们研究了Abraham等人[4]提出的协议，并在Afek等人[5]中进行了研究。我们表明，在一般情况下，该协议仅对次线性大小的联盟具有弹性。具体来说，我们表明Ω(p n logn)随机定位的处理器或Ω(3√n)对抗定位的处理器可以强制任何结果。我们通过证明协议对任何规模为O(4√n)的对抗联盟都具有弹性来补充这一点。我们提出了对协议的修改，并通过展示攻击和弹性结果来证明它对每个规模为O(√n)的联盟都具有弹性。对于每一个k≥1，我们定义了一个图族Gk，可以用树来模拟，其中树中的每个节点最多模拟k个处理器。我们证明，对于Gk中的每个图，不存在对规模为k的联盟具有弹性的公平领导人选举协议。我们的结果推广了Abraham等人[4]先前的结果，该结果表明，对于每个图，不存在对规模为?n/2 ?的联盟具有弹性的公平领导人选举协议。
{"title":"Fair Leader Election for Rational Agents in Asynchronous Rings and Networks","authors":"A. Yifrach, Y. Mansour","doi":"10.1145/3212734.3212767","DOIUrl":"https://doi.org/10.1145/3212734.3212767","url":null,"abstract":"We study a game theoretic model where a coalition of processors might collude to bias the outcome of the protocol, where we assume that the processors always prefer any legitimate outcome over a non-legitimate one. We show that the problems of Fair Leader Election and Fair Coin Toss are equivalent, and focus on Fair Leader Election. Our main focus is on a directed asynchronous ring of n processors, where we investigate the protocol proposed by Abraham et al. [4] and studied in Afek et al. [5]. We show that in general the protocol is resilient only to sub-linear size coalitions. Specifically, we show that Ω( p n logn) randomly located processors or Ω( 3 √ n) adversarially located processors can force any outcome. We complement this by showing that the protocol is resilient to any adversarial coalition of size O( 4 √ n). We propose a modification to the protocol, and show that it is resilient to every coalition of size ?( √ n), by exhibiting both an attack and a resilience result. For every k ≥ 1, we define a family of graphs Gk that can be simulated by trees where each node in the tree simulates at most k processors. We show that for every graph in Gk , there is no fair leader election protocol that is resilient to coalitions of size k. Our result generalizes a previous result of Abraham et al. [4] that states that for every graph, there is no fair leader election protocol which is resilient to coalitions of size ?n/2 ?.","PeriodicalId":198284,"journal":{"name":"Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing","volume":"205 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123019695","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
U. Agarwal, V. Ramachandran, Valerie King, Matteo Pontecorvi
We present a deterministic distributed algorithm to compute all-pairs shortest paths (APSP) in an edge-weighted directed or undirected graph. Our algorithm runs in Õ (n^3/2 ) rounds in the Congest model, where n is the number of nodes in the graph. This is the first o(n^2) rounds deterministic distributed algorithm for the weighted APSP problem. Our algorithm is fairly simple and incorporates a deterministic distributed algorithm we develop for computing a 'blocker set' [King99], which has been used earlier in sequential dynamic computation of APSP.
{"title":"A Deterministic Distributed Algorithm for Exact Weighted All-Pairs Shortest Paths in Õ(n 3/2 ) Rounds","authors":"U. Agarwal, V. Ramachandran, Valerie King, Matteo Pontecorvi","doi":"10.1145/3212734.3212773","DOIUrl":"https://doi.org/10.1145/3212734.3212773","url":null,"abstract":"We present a deterministic distributed algorithm to compute all-pairs shortest paths (APSP) in an edge-weighted directed or undirected graph. Our algorithm runs in Õ (n^3/2 ) rounds in the Congest model, where n is the number of nodes in the graph. This is the first o(n^2) rounds deterministic distributed algorithm for the weighted APSP problem. Our algorithm is fairly simple and incorporates a deterministic distributed algorithm we develop for computing a 'blocker set' [King99], which has been used earlier in sequential dynamic computation of APSP.","PeriodicalId":198284,"journal":{"name":"Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123373933","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The computation of the diameter is one of the most central problems in distributed computation. In the standard CONGEST model, in which two adjacent nodes can exchange O(log n) bits per round (here n denotes the number of nodes of the network), it is known that exact computation of the diameter requires Ω(n) rounds, even in networks with constant diameter. In this paper we investigate quantum distributed algorithms for this problem in the quantum CONGEST model, where two adjacent nodes can exchange O(log n) quantum bits per round. Our main result is a O(√D )-round quantum distributed algorithm for exact diameter computation, where D denotes the diameter. This shows a separation between the computational power of quantum and classical algorithms in the CONGEST model. We also show an unconditional lower bound Ω(√ ) on the round complexity of any quantum algorithm computing the diameter, and furthermore show a tight lower bound Ω(√D ) for any distributed quantum algorithm in which each node can use only poly(log n) quantum bits of memory.
{"title":"Sublinear-Time Quantum Computation of the Diameter in CONGEST Networks","authors":"F. Gall, F. Magniez","doi":"10.1145/3212734.3212744","DOIUrl":"https://doi.org/10.1145/3212734.3212744","url":null,"abstract":"The computation of the diameter is one of the most central problems in distributed computation. In the standard CONGEST model, in which two adjacent nodes can exchange O(log n) bits per round (here n denotes the number of nodes of the network), it is known that exact computation of the diameter requires Ω(n) rounds, even in networks with constant diameter. In this paper we investigate quantum distributed algorithms for this problem in the quantum CONGEST model, where two adjacent nodes can exchange O(log n) quantum bits per round. Our main result is a O(√D )-round quantum distributed algorithm for exact diameter computation, where D denotes the diameter. This shows a separation between the computational power of quantum and classical algorithms in the CONGEST model. We also show an unconditional lower bound Ω(√ ) on the round complexity of any quantum algorithm computing the diameter, and furthermore show a tight lower bound Ω(√D ) for any distributed quantum algorithm in which each node can use only poly(log n) quantum bits of memory.","PeriodicalId":198284,"journal":{"name":"Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing","volume":"222 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116836413","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Dan Alistarh, Christopher De Sa, Nikola Konstantinov
Stochastic Gradient Descent (SGD) is a fundamental algorithm in machine learning, representing the optimization backbone for training several classic models, from regression to neural networks. Given the recent practical focus on distributed machine learning, significant work has been dedicated to the convergence properties of this algorithm under the inconsistent and noisy updates arising from execution in a distributed environment. However, surprisingly, the convergence properties of this classic algorithm in the standard shared-memory model are still not well-understood. In this work, we address this gap, and provide new convergence bounds for lock-free concurrent stochastic gradient descent, executing in the classic asynchronous shared memory model, against a strong adaptive adversary. Our results give improved upper and lower bounds on the "price of asynchrony'' when executing the fundamental SGD algorithm in a concurrent setting. They show that this classic optimization tool can converge faster and with a wider range of parameters than previously known under asynchronous iterations. At the same time, we exhibit a fundamental trade-off between the maximum delay in the system and the rate at which SGD can converge, which governs the set of parameters under which this algorithm can still work efficiently.
{"title":"The Convergence of Stochastic Gradient Descent in Asynchronous Shared Memory","authors":"Dan Alistarh, Christopher De Sa, Nikola Konstantinov","doi":"10.1145/3212734.3212763","DOIUrl":"https://doi.org/10.1145/3212734.3212763","url":null,"abstract":"Stochastic Gradient Descent (SGD) is a fundamental algorithm in machine learning, representing the optimization backbone for training several classic models, from regression to neural networks. Given the recent practical focus on distributed machine learning, significant work has been dedicated to the convergence properties of this algorithm under the inconsistent and noisy updates arising from execution in a distributed environment. However, surprisingly, the convergence properties of this classic algorithm in the standard shared-memory model are still not well-understood. In this work, we address this gap, and provide new convergence bounds for lock-free concurrent stochastic gradient descent, executing in the classic asynchronous shared memory model, against a strong adaptive adversary. Our results give improved upper and lower bounds on the \"price of asynchrony'' when executing the fundamental SGD algorithm in a concurrent setting. They show that this classic optimization tool can converge faster and with a wider range of parameters than previously known under asynchronous iterations. At the same time, we exhibit a fundamental trade-off between the maximum delay in the system and the rate at which SGD can converge, which governs the set of parameters under which this algorithm can still work efficiently.","PeriodicalId":198284,"journal":{"name":"Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124321806","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We present a randomized distributed algorithm that computes a Δ- coloring in any non-complete graph with maximum degree Δ ≥ 4 in O(log Δ) +2O( √ log log n) rounds, as well as a randomized algorithm that computes a Δ-coloring in O((log logn)2) rounds when Δ ε [3,O(1)]. Both these algorithms improve on an O(log3 n/ log Δ)- round algorithm of Panconesi and Srinivasan [STOC'1993], which has remained the state of the art for the past 25 years. Moreover, the latter algorithm gets (exponentially) closer to an Ω(log logn) round lower bound of Brandt et al. [STOC'16].
{"title":"Improved Distributed Delta-Coloring","authors":"M. Ghaffari, J. Hirvonen, F. Kuhn, Yannic Maus","doi":"10.1145/3212734.3212764","DOIUrl":"https://doi.org/10.1145/3212734.3212764","url":null,"abstract":"We present a randomized distributed algorithm that computes a Δ- coloring in any non-complete graph with maximum degree Δ ≥ 4 in O(log Δ) +2O( √ log log n) rounds, as well as a randomized algorithm that computes a Δ-coloring in O((log logn)2) rounds when Δ ε [3,O(1)]. Both these algorithms improve on an O(log3 n/ log Δ)- round algorithm of Panconesi and Srinivasan [STOC'1993], which has remained the state of the art for the past 25 years. Moreover, the latter algorithm gets (exponentially) closer to an Ω(log logn) round lower bound of Brandt et al. [STOC'16].","PeriodicalId":198284,"journal":{"name":"Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing","volume":"97 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121118128","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
S. Goldwasser, R. Ostrovsky, Alessandra Scafuro, Adam Sealfon
We introduce a new coordination problem in distributed computing that we call the population stability problem. A system of agents each with limited memory and communication, as well as the ability to replicate and self-destruct, is subjected to attacks by a worst-case adversary that can at a bounded rate (1) delete agents chosen arbitrarily and (2) insert additional agents with arbitrary initial state into the system. The goal is perpetually to maintain a population whose size is within a constant factor of the target size N. The problem is inspired by the ability of complex biological systems composed of a multitude of memory-limited individual cells to maintain a stable population size in an adverse environment. Such biological mechanisms allow organisms to heal after trauma or to recover from excessive cell proliferation caused by inflammation, disease, or normal development. We present a population stability protocol in a communication model that is a synchronous variant of the population model of Angluin et al. In each round, pairs of agents selected at random meet and exchange messages, where at least a constant fraction of agents is matched in each round. Our protocol uses three-bit messages and ω(log^2 N) states per agent. We emphasize that our protocol can handle an adversary that can both insert and delete agents, a setting in which existing approximate counting techniques do not seem to apply. The protocol relies on a novel coloring strategy in which the population size is encoded in the variance of the distribution of colors. Individual agents can locally obtain a weak estimate of the population size by sampling from the distribution, and make individual decisions that robustly maintain a stable global population size.
{"title":"Population Stability: Regulating Size in the Presence of an Adversary","authors":"S. Goldwasser, R. Ostrovsky, Alessandra Scafuro, Adam Sealfon","doi":"10.1145/3212734.3212747","DOIUrl":"https://doi.org/10.1145/3212734.3212747","url":null,"abstract":"We introduce a new coordination problem in distributed computing that we call the population stability problem. A system of agents each with limited memory and communication, as well as the ability to replicate and self-destruct, is subjected to attacks by a worst-case adversary that can at a bounded rate (1) delete agents chosen arbitrarily and (2) insert additional agents with arbitrary initial state into the system. The goal is perpetually to maintain a population whose size is within a constant factor of the target size N. The problem is inspired by the ability of complex biological systems composed of a multitude of memory-limited individual cells to maintain a stable population size in an adverse environment. Such biological mechanisms allow organisms to heal after trauma or to recover from excessive cell proliferation caused by inflammation, disease, or normal development. We present a population stability protocol in a communication model that is a synchronous variant of the population model of Angluin et al. In each round, pairs of agents selected at random meet and exchange messages, where at least a constant fraction of agents is matched in each round. Our protocol uses three-bit messages and ω(log^2 N) states per agent. We emphasize that our protocol can handle an adversary that can both insert and delete agents, a setting in which existing approximate counting techniques do not seem to apply. The protocol relies on a novel coloring strategy in which the population size is encoded in the variance of the distribution of colors. Individual agents can locally obtain a weak estimate of the population size by sampling from the distribution, and make individual decisions that robustly maintain a stable global population size.","PeriodicalId":198284,"journal":{"name":"Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128018485","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. Ghaffari, Themis Gouleakis, Slobodan Mitrovic, R. Rubinfeld
We present O(loglog n) -round algorithms in the Massively Parallel Computation (MPC) model, with Õ (n) memory per machine, that compute a maximal independent set, a 1+ε approximation of maximum matching, and a 2+εapproximation of minimum vertex cover, for any n-vertex graph and any constant eps>0. These improve the state of the art as follows: Our MIS algorithm leads to a simple O(loglog Δ)-round MIS algorithm in the CONGESTED-CLIQUE model of distributed computing, which improves on the Õ (√log Δ )-round algorithm of Ghaffari [PODC'17]. Our O(loglog n)-round (1+ε)-approximate maximum matching algorithm simplifies or improves on the following prior work: O(log^2log n)-round (1+eps)-approximation algorithm of Czumaj et al. [STOC'18] and $O(loglog n)-round (1+ε)-approximation algorithm of Assadi et al. [arXiv'17]. Our O(loglog n)-round (2+ε)-approximate minimum vertex cover algorithm improves on an O(loglog n)-round O(1)-approximation of Assadi et al. [arXiv'17].
{"title":"Improved Massively Parallel Computation Algorithms for MIS, Matching, and Vertex Cover","authors":"M. Ghaffari, Themis Gouleakis, Slobodan Mitrovic, R. Rubinfeld","doi":"10.1145/3212734.3212743","DOIUrl":"https://doi.org/10.1145/3212734.3212743","url":null,"abstract":"We present O(loglog n) -round algorithms in the Massively Parallel Computation (MPC) model, with Õ (n) memory per machine, that compute a maximal independent set, a 1+ε approximation of maximum matching, and a 2+εapproximation of minimum vertex cover, for any n-vertex graph and any constant eps>0. These improve the state of the art as follows: Our MIS algorithm leads to a simple O(loglog Δ)-round MIS algorithm in the CONGESTED-CLIQUE model of distributed computing, which improves on the Õ (√log Δ )-round algorithm of Ghaffari [PODC'17]. Our O(loglog n)-round (1+ε)-approximate maximum matching algorithm simplifies or improves on the following prior work: O(log^2log n)-round (1+eps)-approximation algorithm of Czumaj et al. [STOC'18] and $O(loglog n)-round (1+ε)-approximation algorithm of Assadi et al. [arXiv'17]. Our O(loglog n)-round (2+ε)-approximate minimum vertex cover algorithm improves on an O(loglog n)-round O(1)-approximation of Assadi et al. [arXiv'17].","PeriodicalId":198284,"journal":{"name":"Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126557758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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