A set of participants that want to agree on a common opinion despite the presence of malicious or Byzantine participants need to solve an instance of a Byzantine agreement problem. This classic problem has been well s...
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ISBN:
(纸本)9781450375825
A set of participants that want to agree on a common opinion despite the presence of malicious or Byzantine participants need to solve an instance of a Byzantine agreement problem. This classic problem has been well studied but most of the existing solutions assume that the participants are aware of n - the total number of participants in the system - and f - the upper bound on the number of Byzantine participants. In this paper, we examine a synchronous system with Byzantine faults where the participants are neither aware of n nor f. The participants have unique identifiers, which are not necessarily consecutive. For such a system, we give algorithms for rotor-coordinator and consensus, both with the resiliency of n > 3f, which is also the optimal resiliency for solving consensus when the participants know n and f. Thus, resiliency is unaffected even if the Byzantine participants can lie about n and f.
Locally checkable labeling problems (LCLs) are distributed graph problems in which a solution is globally feasible if it is locally feasible in all constant-radius neighborhoods. Vertex colorings, maximal independent ...
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ISBN:
(纸本)9781450375825
Locally checkable labeling problems (LCLs) are distributed graph problems in which a solution is globally feasible if it is locally feasible in all constant-radius neighborhoods. Vertex colorings, maximal independent sets, and maximal matchings are examples of LCLs. On the one hand, it is known that some LCLs benefit exponentially from randomness-for example, any deterministic distributed algorithm that finds a sinkless orientation requires Theta(logn) rounds in the LOCAL model, while the randomized complexity of the problem is Theta(log logn) rounds. On the other hand, there are also many LCLs in which randomness is useless. Previously, it was not known whether there are any LCLs that benefit from randomness, but only subexponentially. We show that such problems exist: for example, there is an LCL with deterministic complexity Theta(log(2) n) rounds and randomized complexity T(logn log logn) rounds.
This paper considers the problem of Byzantine fault-tolerance in distributed multi-agent optimization. In this problem, each agent has a local cost function. The goal of a distributed optimization algorithm is to allo...
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ISBN:
(纸本)9781450375825
This paper considers the problem of Byzantine fault-tolerance in distributed multi-agent optimization. In this problem, each agent has a local cost function. The goal of a distributed optimization algorithm is to allow the agents to collectively compute a minimum of their aggregate cost function. We consider the case when a certain number of agents may be Byzantine faulty. Such faulty agents may not follow a prescribed algorithm, and they may send arbitrary or incorrect information regarding their local cost functions. Unless a fault-tolerance mechanism is employed, traditional distributed optimization algorithms cannot tolerate such faulty agents. A reasonable goal in presence of faulty agents is to minimize the aggregate cost of the non-faulty agents. However, we show that this goal is impossible to achieve unless the cost functions of the non-faulty agents have a minimal redundancy property. We further propose a distributed optimization algorithm that allows the non-faulty agents to obtain a minimum of their aggregate cost if the minimal redundancy property holds. The scope of our algorithm is demonstrated through distributed sensing and learning applications, which are special cases of distributed optimization.
Convolution is the most time-consuming part in the computation of convolutional neural networks (CNNs), which have achieved great successes in numerous practical applications. Due to the complex data dependency and th...
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ISBN:
(纸本)9781450382946
Convolution is the most time-consuming part in the computation of convolutional neural networks (CNNs), which have achieved great successes in numerous practical applications. Due to the complex data dependency and the increase in the amount of model samples, the convolution suffers from high overhead on data movement (i.e., memory access). This work provides comprehensive analysis and methodologies to minimize the communication for the convolution in CNNs. With an in-depth analysis of the recent I/O complexity theory under the red-blue game model, we develop a general I/O lower bound theory for a composite algorithm which consists of several different sub-computations. Based on the proposed theory, we establish the data movement lower bound results for two main convolution algorithms in CNNs, namely the direct convolution and Winograd algorithm, which represents the direct and indirect implementations of a convolution respectively. Next, derived from I/O lower bound results, we design the near I/O-optimal dataflow strategies for the two main convolution algorithms by fully exploiting the data reuse. Furthermore, in order to push the envelope of performance of the near I/O-optimal dataflow strategies further, an aggressive design of auto-tuning based on I/O lower bounds, is proposed to search an optimal parameter configuration for the direct convolution and Winograd algorithm on GPU, such as the number of threads and the size of shared memory used in each thread block. Finally, experiment evaluation results on the direct convolution and Winograd algorithm show that our dataflow strategies with the auto-tuning approach can achieve about 3.32× performance speedup on average over cuDNN. In addition, compared with TVM, which represents the state-of-the-art technique for auto-tuning, not only our auto-tuning method based on I/O lower bounds can find the optimal parameter configuration faster, but also our solution has higher performance than the optimal solution provided
We improve the time complexity of the single-source shortest path problem for weighted directed graphs (with non-negative integer weights) in the Broadcast CONGEST model of distributedcomputing. For polynomially boun...
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ISBN:
(纸本)9781450375825
We improve the time complexity of the single-source shortest path problem for weighted directed graphs (with non-negative integer weights) in the Broadcast CONGEST model of distributedcomputing. For polynomially bounded edge weights, the state-of-the-art algorithm for this problem requires (O) over tilde (min root nD(1/2), root nD(1/4) +n(3/5) + D}) rounds [Forster and Nanongkai, FOCS 2018], which is quite far from the known lower bound of (O) over tilde(root n + D) rounds [Elkin, STOC 2014];here D is the diameter of the underlying network and n is the number of vertices in it. For the approximate version of this problem, Forster and Nanongkai [FOCS 2018] obtained an upper bound of (O) over tilde (root nD(1/4) + D), and stated that achieving the same bound for the exact case remains a major open problem. In this paper we resolve the above mentioned problem by devising a new randomized algorithm for solving (the exact version of) this problem in (O) over tilde(root nD(1/4) + D) rounds. Our algorithm is based on a novel weight-modifying technique that allows us to compute bounded-hop distance approximation that preserves a certain form of the triangle inequality for the edges in the graph.
Round-based models are very common message-passing models;combinatorial topology applied to distributedcomputing provides sweeping results like general lower bounds. We combine both to study the computability of k -s...
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ISBN:
(纸本)9781450375825
Round-based models are very common message-passing models;combinatorial topology applied to distributedcomputing provides sweeping results like general lower bounds. We combine both to study the computability of k -set agreement. Among all the possible round-based models, we consider oblivious ones, where the constraints are given only round per round by a set of allowed graphs. And among oblivious models, we focus on closed-above ones, that is models where the set of possible graphs contains all graphs with more edges than some starting graphs. These capture intuitively the underlying structure required by some communication model, like containing a ring. We then derive lower bounds and upper bounds in one round for k-set agreement, such that these bounds are proved using combinatorial topology but stated only in terms of graph properties. These bounds extend to multiple rounds when limiting our algorithms to be oblivious - recalling only pairs of processes and initial value, not who send what and when.
We show that the (degree + 1)-list coloring problem can be solved deterministically in O(D . log n . log(2) Delta) rounds in the CONGEST model, where D is the diameter of the graph, n the number of nodes, and Delta th...
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ISBN:
(纸本)9781450375825
We show that the (degree + 1)-list coloring problem can be solved deterministically in O(D . log n . log(2) Delta) rounds in the CONGEST model, where D is the diameter of the graph, n the number of nodes, and Delta the maximum degree. Using the recent polylogarithmic-time deterministic network decomposition algorithm by Rozhon and Ghaffari [49], this implies the first efficient (i.e., poly log n-time) deterministic CONGEST algorithm for the (Delta + 1)-coloring and the (degree + 1)-list coloring problem. Previously the best known algorithm required 2(O(root log n)) rounds and was not based on network decompositions. Our techniques also lead to deterministic (degree + 1)-list coloring algorithms for the congested clique and the massively parallel computation (MPC) model. For the congested clique, we obtain an algorithm with time complexity O(log Delta . log log Delta), for the MPC model, we obtain algorithms with round complexity O(log(2) Delta) for the linear-memory regime and O(log(2) Delta + log n) for the sublinear memory regime.
We study the effect of noise on the n-party beeping model. In this model, in every round, each party may decide to either 'beep' or not. All parties hear a beep if and only if at least one party beeps. The bee...
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ISBN:
(纸本)9781450375825
We study the effect of noise on the n-party beeping model. In this model, in every round, each party may decide to either 'beep' or not. All parties hear a beep if and only if at least one party beeps. The beeping model is becoming increasingly popular, as it offers a very simple abstraction of wireless networks and is very well suited for studying biological phenomena. Still, the noise resilience of the beeping model is yet to be understood. Our main result is a lower bound, showing that making protocols in the beeping model resilient to noise may have a large performance overhead. Specifically, we give a protocol that works over the (noiseless) beeping model, and prove that any scheme that simulates this protocol over the beeping model with correlated stochastic noise will blow up the number of rounds by an O(logn) multiplicative factor. We complement this result by a matching upper bound, constructing a noise-resilient simulation scheme with O(logn) overhead for any noiseless beeping protocol.
We present improved algorithms for approximating maximum-weight independent set (MaxIS) in the CONGEST model. Given an input graph, let n and Delta be the number of nodes and maximum degree, respectively, and let MIS(...
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ISBN:
(纸本)9781450375825
We present improved algorithms for approximating maximum-weight independent set (MaxIS) in the CONGEST model. Given an input graph, let n and Delta be the number of nodes and maximum degree, respectively, and let MIS(n,Delta ) be the running time of finding a maximal independent set (MIS) in the CONGEST model. Bar-Yehuda et al. [PODC 2017] showed that there is an algorithm in the CONGEST model that finds a.-approximation for MaxIS in O ( MIS(n,Delta) log W) rounds, where.. is the maximum weight of a node in the graph, which can be as high as poly(n). Whether their algorithm is deterministic or randomized depends on the MIS algorithm that is used as a black-box. Our results: (1) A deterministic O(MIS(n, Delta)/epsilon)-round algorithm that finds a (1 + epsilon)Delta-approximation for MaxIS in the CONGEST model. (2) Arandomized ( poly( log log n)/epsilon)-round algorithm that finds, with high probability, a (1 +epsilon)Delta-approximation for MaxIS in the CONGEST model. That is, by sacrificing only a tiny fraction of the approximation guarantee, we achieve an exponential speed-up in the running time over the previous best known result.
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