On the power of the congested clique model

Drucker, Andrew; Kühn, Fabian; Oshman, Rotem

doi:10.1145/2611462.2611493

Cited by 179 publications

(216 citation statements)

References 56 publications

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“…Perhaps the closest model to the present work is the "congested clique" model, the special case of the CONGEST model [31] in which each pair of machines is connected by a direct link (see [11] and the references therein). The original motivation of this model was for the design and analysis of distributed algorithms, but it is also relevant to massively parallel computation.…”

Section: Relation To Other Computational Modelsmentioning

confidence: 99%

Shuffles and Circuits

Roughgarden

Vassilvitskii

Wang

2016

Proceedings of the 28th ACM Symposium on Parallelism in Algorithms and Architectures

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The goal of this paper is to identify fundamental limitations on how efficiently algorithms implemented on platforms such as MapReduce and Hadoop can compute the central problems in the motivating application domains, such as graph connectivity problems.We introduce an abstract model of massively parallel computation, where essentially the only restrictions are that the "fan-in" of each machine is limited to s bits, where s is smaller than the input size n, and that computation proceeds in synchronized rounds, with no communication between different machines within a round. Lower bounds on the round complexity of a problem in this model apply to every computing platform that shares the most basic design principles of MapReduce-type systems.We prove that computations in our model that use few rounds can be represented as low-degree polynomials over the reals. This connection allows us to translate a lower bound on the (approximate) polynomial degree of a Boolean function to a lower bound on the round complexity of every (randomized) massively parallel computation of that function. These lower bounds apply even in the "unbounded width" version of our model, where the number of machines can be arbitrarily large. As one example of our general results, computing any non-trivial monotone graph propertysuch as connectivity -requires a super-constant number of rounds when every machine can accept only a sub-polynomial (in n) number of input bits s.Finally, we prove that, in two senses, our lower bounds are the best one could hope for. For the unbounded-width model, we prove a matching upper bound. Restricting to a polynomial number of machines, we show that asymptotically better lower bounds require proving that P = N C 1 .

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Section: Relation To Other Computational Modelsmentioning

confidence: 99%

Shuffles and Circuits

Roughgarden

Vassilvitskii

Wang

2016

Proceedings of the 28th ACM Symposium on Parallelism in Algorithms and Architectures

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“…This work Prior work matrix multiplication (semiring) O(n 1/3 ) -matrix multiplication (ring) O(n 0.158 ) O(n 0.373 ) [25] triangle counting O(n 0.158 ) O(n 1/3 / log n) [24] (1))-approximationÕ(n 1/2 ) [57] unweighted, undirected APSP O(n 0.158 ) -· (2 + o(1))-approximationÕ(n 1/2 )…”

Section: Problemmentioning

confidence: 99%

“…Analogously with the matrix multiplication exponent, we denote by ρ the exponent of matrix multiplication in the congested clique model, that is, the infimum over all values σ such that there exists a matrix multiplication algorithm in the congested clique running in O(n σ ) rounds. In this notation, Theorem 1 gives us ρ ≤ 1 − 2/ω < 0.15715 ; prior to this work, it was known that ρ ≤ ω − 2 [25]. For the rest of this paper, we will -analogously with the convention in centralised algorithmics -slightly abuse this notation by writing n ρ for the complexity of matrix multiplication in the congested clique.…”

Section: Matrix Multiplication On a Congested Cliquementioning

confidence: 99%

“…Recall that the girth g of an undirected unweighted graph G = (V, E) is the length of the shortest cycle in G. To compute the girth in the congested clique model, we leverage the fast cycle detection algorithm and the following lemma giving a trade-off between the girth and the number of edges. A similar approach of bounding from above the number of edges of a graph that contains no copies of some given subgraph was taken by Drucker et al [25].…”

Section: Girthmentioning

confidence: 99%

“…As such, it has been recently gaining increasing attention [24,25,36,37,46,49,51,57,59,63], in an attempt to understand the relative computational power of distributed computing models.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Algebraic Methods in the Congested Clique

Censor-Hillel

Kaski

Korhonen

et al. 2015

Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing

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In this work, we use algebraic methods for studying distance computation and subgraph detection tasks in the congested clique model. Specifically, we adapt parallel matrix multiplication implementations to the congested clique, obtaining an O(n 1−2/ω ) round matrix multiplication algorithm, where ω < 2.3728639 is the exponent of matrix multiplication. In conjunction with known techniques from centralised algorithmics, this gives significant improvements over previous best upper bounds in the congested clique model. The highlight results include: In addition, we present a novel constant-round combinatorial algorithm for detecting 4-cycles.

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Robust reconstruction of Barabási‐Albert networks in the broadcast congested clique model

et al. 2015

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In the broadcast version of the congested clique model, n nodes communicate in synchronous rounds by writing O(log n)-bit messages on a whiteboard, which is visible to all of them. The joint input to the nodes is an undirected n-node graph G, with node i receiving the list of its neighbors in G. Our goal is to design a protocol at the end of which the information contained in the whiteboard is enough for reconstructing G. It has already been shown that there is a one-round protocol for reconstructing graphs with bounded degeneracy. The main drawback of that protocol is that the degeneracy m of the input graph G must be known a priori by the nodes. Moreover, the protocol fails when applied to graphs with degeneracy larger than m. In this paper we address this issue by looking for robust reconstruction protocols, that is, protocols which always give the correct answer and work efficiently when the input is restricted to a certain class. We introduce a very simple, two-round protocol that we call Robust-Reconstruction. We prove that this protocol is robust for reconstructing the class of Barabási-Albert trees with (expected) message size O(log n). Moreover, we present computational evidence suggesting that Robust-Reconstruction also generates logarithmic size messages for arbitrary Barabási-Albert networks. Finally, we stress the importance of the preferential attachment mechanism (used in the construction of Barabási-Albert networks) by proving that RobustReconstruction does not generate short messages for random recursive 1 trees.

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On the power of the congested clique model

Cited by 179 publications

References 56 publications

Shuffles and Circuits

Shuffles and Circuits

Algebraic Methods in the Congested Clique

Robust reconstruction of Barabási‐Albert networks in the broadcast congested clique model

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