We present a time-optimal deterministic distributed algorithm for approximating a minimum weight vertex cover in hypergraphs of rank f. This problem is equivalent to the Minimum Weight Set Cover problem in which the f...
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ISBN:
(纸本)9781450362177
We present a time-optimal deterministic distributed algorithm for approximating a minimum weight vertex cover in hypergraphs of rank f. This problem is equivalent to the Minimum Weight Set Cover problem in which the frequency of every element is bounded by f. The approximation factor of our algorithm is (f + epsilon). Let Delta denote the maximum degree in the hypergraph. Our algorithm runs in the congest model and requires O(log Delta/log log Delta) rounds, for constants epsilon is an element of (0, 1] and f is an element of N+. This is the first distributed algorithm for this problem whose running time does not depend on the vertex weights nor the number of vertices. Thus adding another member to the exclusive family of provably optimal distributed algorithms. For constant values of f and epsilon, our algorithm improves over the (f + epsilon)-approximation algorithm of [16] whose running time is O(log Delta + log W), where W is the ratio between the largest and smallest vertex weights in the graph. Our algorithm also achieves an f-approximation for the problem in O(f log n) rounds, improving over the classical result of [13] that achieves a running time of O(f log(2) n). Finally, for weighted vertex cover (f = 2) our algorithm achieves a deterministic running time of O(log n), matching the randomized previously best result of [14]. We also show that integer covering-programs can be reduced to the Minimum Weight Set Cover problem in the distributed setting. This allows us to achieve an (f + epsilon)-approximate integral solution in O((1 + f/logn) center dot (log Delta/log log Delta + (f center dot logM)(1.01) center dot log epsilon(-1) center dot (log Delta)(0.01))) rounds, where f bounds the number of variables in a constraint, Delta bounds the number of constraints a variable appears in, and M = max {1, inverted right perpendicular1/a(min)inverted left perpendicular}, where amin is the smallest normalized constraint coefficient. This significantly improves over t
This paper considers the Byzantine consensus problem for nodes with binary inputs. The nodes are interconnected by a network represented as an undirected graph, and the system is assumed to be synchronous. Under the c...
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ISBN:
(纸本)9781450362177
This paper considers the Byzantine consensus problem for nodes with binary inputs. The nodes are interconnected by a network represented as an undirected graph, and the system is assumed to be synchronous. Under the classical point-to-point communication model, it is well-known that the following two conditions are both necessary and sufficient to achieve Byzantine consensus among n nodes in the presence of up to f Byzantine faulty nodes: n >= 3f + 1 and vertex connectivity at least 2f +1. In the classical point-to-point communication model, it is possible for a faulty node to equivocate, i.e., transmit conflicting information to different neighbors. Such equivocation is possible because messages sent by a node to one of its neighbors are not overheard by other neighbors. This paper considers the local broadcast model. In contrast to the point-to-point communication model, in the local broadcast model, messages sent by a node are received identically by all of its neighbors. Thus, under the local broadcast model, attempts by a node to send conflicting information can be detected by its neighbors. Under this model, we show that the following two conditions are both necessary and sufficient for Byzantine consensus: vertex connectivity at least left perpendicular3f /2right perpendicular + 1 and minimum node degree at least 2f. Observe that the local broadcast model results in a lower requirement for connectivity and the number of nodes n, as compared to the point-to-point communication model. We extend the above results to a hybrid model that allows some of the Byzantine faulty nodes to equivocate. The hybrid model bridges the gap between the point-to-point and local broadcast models, and helps to precisely characterize the trade-off between equivocation and network requirements.
We study linear programming and general LP-type problems in several big data (streaming and distributed) models. We mainly focus on low dimensional problems in which the number of constraints is much larger than the n...
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ISBN:
(纸本)9781450362276
We study linear programming and general LP-type problems in several big data (streaming and distributed) models. We mainly focus on low dimensional problems in which the number of constraints is much larger than the number of variables. Low dimensional LP-type problems appear frequently in various machine learning tasks such as robust regression, support vector machines, and core vector machines. As supporting large-scale machine learning queries in database systems has become an important direction for database research, obtaining efficient algorithms for low dimensional LP-type problems on massive datasets is of great value. In this paper we give both upper and lower bounds for LP-type problems in distributed and streaming models. Our bounds are almost tight when the dimensionality of the problem is a fixed constant.
In this work, we propose an IoT edge-based energy management system devoted to minimizing the energy cost for the daily-use of in-home appliances. The proposed approach employs a load scheduling based on a load shifti...
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In this work, we propose an IoT edge-based energy management system devoted to minimizing the energy cost for the daily-use of in-home appliances. The proposed approach employs a load scheduling based on a load shifting technique, and it is designed to operate in an edge-computing environment naturally. The scheduling considers all together time-variable profiles for energy cost, energy production, and energy consumption for each shiftable appliance. Deadlines for load termination can also be expressed. In order to address these goals, the scheduling problem is formulated as a Markov decision process and then processed through a reinforcement learning technique. The approach is validated by the development of an agent-based real-world test case deployed in an edge context.
The interest in formal methods and verification of correctness-critical distributed systems is on the rise in the past few years. But what are the gains from proving statements about software in full mathematical rigo...
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ISBN:
(纸本)9781450362177
The interest in formal methods and verification of correctness-critical distributed systems is on the rise in the past few years. But what are the gains from proving statements about software in full mathematical rigour? Do they justify the high cost of verification? And how far can we extend our trust in formal methods when talking about realistic distributed systems and their client programs?This talk is in three parts. First, I will provide an overview of the state of the art in machine-assisted reasoning about distributed consensus protocols, their implementations, and applications. Next, I will discuss the trade-offs that have to be made in order to enable mechanised proofs about runnable systems code, as well as implications of the assumptions made to describe the real-world execution environments. Lastly, I will focus on the ongoing work propelled by the programming languages community towards engineering modular proofs about distributed protocols-a way to build correct-by-construction composite systems from verified reusable components.
We present Min-Rounds BC (MRBC), a distributed-memory algorithm in the CONGEST model that computes the betweenness centrality (BC) of every vertex in a directed unweighted n-node graph in O(n) rounds. Min-Rounds BC al...
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ISBN:
(纸本)9781450362252
We present Min-Rounds BC (MRBC), a distributed-memory algorithm in the CONGEST model that computes the betweenness centrality (BC) of every vertex in a directed unweighted n-node graph in O(n) rounds. Min-Rounds BC also computes all-pairs-shortest-paths (APSP) in such graphs. It improves the number of rounds by at least a constant factor over previous results for unweighted directed APSP and for unweighted BC, both directed and undirected. We implemented MRBC in D-Galois, a state-of-the-art distributed graph analytics system, incorporated additional optimizations enabled by the D-Galois model, and evaluated its performance on a production cluster with up to 256 hosts using power-law and road networks. Compared to the BC algorithm of Brandes, on average, MRBC reduces the number of rounds by 14.0x and the communication time by 2.8x for the graphs in our test suite. As a result, MRBC is 2.1x faster on average than Brandes BC for real-world web-crawls on 256 hosts.
Vizing showed that it suffices to color the edges of a simple graph using Delta + 1 colors, where Delta is the maximum degree of the graph. However, up to this date, no efficient distributed edge-coloring algorithm is...
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ISBN:
(纸本)9781450367059
Vizing showed that it suffices to color the edges of a simple graph using Delta + 1 colors, where Delta is the maximum degree of the graph. However, up to this date, no efficient distributed edge-coloring algorithm is known for obtaining such coloring, even for constant degree graphs. The current algorithms that get closest to this number of colors are the randomized (Delta + (Theta) over tilde(root Delta))-edge-coloring algorithm that runs in polylog( n) rounds by Chang et al. [SODA 2018] and the deterministic (Delta + polylog(n))-edge-coloring algorithm that runs in poly(Delta, log n) rounds by Ghaffari et al. [STOC 2018]. We present two distributed edge-coloring algorithms that run in poly(Delta, log n) rounds. The first algorithm, with randomization, uses only Delta + 2 colors. The second algorithm is a deterministic algorithm that uses Delta + O(log n/log log n) colors. Our approach is to reduce the distributed edge-coloring problem into an online and restricted version of balls-into-bins problem. If l is the maximum load of the bins, our algorithm uses Delta + 2l - 1 colors. We show how to achieve l = 1 with randomization and l = O(log n/log log n) without randomization.
Gaussian Processes (GPs) are powerful non-parametric Bayesian models for function estimation, but suffer from high complexity in terms of both computation and storage. To address such issues, approximation methods hav...
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ISBN:
(纸本)9781450359337
Gaussian Processes (GPs) are powerful non-parametric Bayesian models for function estimation, but suffer from high complexity in terms of both computation and storage. To address such issues, approximation methods have flourished in the literature, including model approximations and approximate inference. However, these methods often sacrifice accuracy for scalability. In this work, we present the design and evaluation of a distributed method for exact GP inference, that achieves true model parallelism using simple, high-level distributedcomputing frameworks. Our experiments show that exact inference at scale is not only feasible, but it also brings substantial benefits in terms of low error rates and accurate quantification of uncertainty.
Communication overhead is a well-known performance bottleneck in distributed Stochastic Gradient Descent (SGD), which is a popular algorithm to perform optimization in large-scale machine learning tasks. In this work,...
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