Topic
Communication complexity
About: Communication complexity is a research topic. Over the lifetime, 3870 publications have been published within this topic receiving 105832 citations.
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Papers
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TL;DR: It is shown that, in arbitrary graphs, any sense of direction has a dramatic effect on the communication complexity of several important distributed problems: Broadcast, Depth First Traversal, Election, and Spanning Tree Construction.
46 citations
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TL;DR: A new integrated method of exploiting model, batch and domain parallelism for the training of deep neural networks (DNNs) on large distributed-memory computers using minibatch stochastic gradient descent (SGD).
Abstract: We propose a new integrated method of exploiting model, batch and domain parallelism for the training of deep neural networks (DNNs) on large distributed-memory computers using minibatch stochastic gradient descent (SGD). Our goal is to find an efficient parallelization strategy for a fixed batch size using $P$ processes. Our method is inspired by the communication-avoiding algorithms in numerical linear algebra. We see $P$ processes as logically divided into a $P_r \times P_c$ grid where the $P_r$ dimension is implicitly responsible for model/domain parallelism and the $P_c$ dimension is implicitly responsible for batch parallelism. In practice, the integrated matrix-based parallel algorithm encapsulates these types of parallelism automatically. We analyze the communication complexity and analytically demonstrate that the lowest communication costs are often achieved neither with pure model nor with pure data parallelism. We also show how the domain parallel approach can help in extending the theoretical scaling limit of the typical batch parallel method.
46 citations
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TL;DR: A threshold signature scheme enables distributed signing among n players such that any subgroup of size $t+1$ can sign, whereas any group with t or fewer players cannot as mentioned in this paper.
Abstract: A threshold signature scheme enables distributed signing among n players such that any subgroup of size $t+1$ can sign, whereas any group with t or fewer players cannot. While there exist previous threshold schemes for the ECDSA signature scheme, we are the first protocol that supports multiparty signatures for any $t leq n$ with an efficient dealerless key generation. Our protocol is faster than previous solutions and significantly reduces the communication complexity as well. We prove our scheme secure against malicious adversaries with a dishonest majority. We implemented our protocol, demonstrating its efficiency and suitability to be deployed in practice.
46 citations
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25 Feb 1993TL;DR: The properties of the complexity measure C b (·) is studied, which is an encoding e: D → {0,1}b, so that for any y, f(x,y) can be determined (quickly) by probing e(x).
Abstract: A static data structure problem consists of a set of data D, a set of queries Q and a function f with domain D × Q. Given a space bound b, a (good) solution to the problem is an encoding e: D → {0,1}b, so that for any y, f(x,y) can be determined (quickly) by probing e(x). The worst case number of probes needed is C b (f), the bit probe complexity of f. We study the properties of the complexity measure C b (·).
46 citations
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07 Jan 2007TL;DR: The communication complexity of finding the longest increasing subsequence (LIS) of a string shared between two parties is considered and tight bounds for the space complexity of randomized one-pass streaming algorithms for this problem are proved.
Abstract: We consider the communication complexity of finding the longest increasing subsequence (LIS) of a string shared between two parties. We prove tight bounds for the space complexity of randomized one-pass streaming algorithms for this problem. Our bounds are parameterized in terms of the LIS of the inputs. This resolves an open question in [19]. We also give the first bounds for approximating the LIS and its length.Next, we consider the communication complexity of finding the longest common subsequece (LCS) of two strings held by different parties, as well as the problem of approximating its length. We improve the existing lower bounds for these problems, even in the most difficult case when both parties have a permutation of N symbols. Our results yield tight space bounds for multipass deterministic streaming algorithms. For randomized mutlipass algorithms, our bounds are tight up to a logarithmic factor.
46 citations