Round compression for parallel matching algorithms

Czumaj, Artur; Łącki, Jakub; Mądry, Aleksander; Mitrović, Slobodan; Onak, Krzysztof; Sankowski, Piotr

doi:10.1145/3188745.3188764

Cited by 55 publications

(46 citation statements)

References 35 publications

(86 reference statements)

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“…To work on truly massive inputs, we ideally want our local space to be sublinear in input size. Some earlier works (e.g., [4,15,19]) study the regime where space is roughly the number of nodes of the graph (i.e., = Θ( )); here, though, we consider the more restrictive low space regime. That is, we give fully scalable algorithms which use only = Θ ( ) space, for any constant > 0.…”

Section: The Mpc Modelmentioning

confidence: 99%

“…The key idea here is to perform deterministic round compression on Luby's algorithm. Round compression is a technique used in some randomized results in MPC and CONGESTED CLIQUE (e.g., [15,19,20], though only the former uses the term), which works by gathering enough information onto machines to simulate multiple steps of a LOCAL or CONGEST algorithm at once.…”

Section: Our Approachmentioning

confidence: 99%

See 1 more Smart Citation

Graph Sparsification for Derandomizing Massively Parallel Computation with Low Space

Czumaj

Davies

Parter

2020

Proceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures

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Section: The Mpc Modelmentioning

confidence: 99%

Section: Our Approachmentioning

confidence: 99%

Graph Sparsification for Derandomizing Massively Parallel Computation with Low Space

Czumaj

Davies

Parter

2020

Proceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures

Self Cite

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“…Massively Parallel Algorithms. There has been a huge body of work on developing efficient, low round-complexity distributed graph algorithms in the Massively Parallel Computation model [3,5,6,9,15,17,18,22,30,36,46,49,60], including many other papers. In this paper, our focus is on recently proposed Adaptive Massively Parallel Computation model [19], which was also recently studied from a lower-bound perspective by Charikar et al [28].…”

Section: Related Workmentioning

confidence: 99%

“…The MPC model has been extensively studied in theory in recent years [3,5,6,9,15,17,18,22,30,36,46,49,60], and its theoretical capabilities and limitations are relatively wellunderstood. In the context of graph algorithms, a significant limitation of the model is, roughly speaking, the fact that initially each node only knows its immediate neighbors, and exploring a larger neighborhood requires multiple rounds.…”

Section: Introductionmentioning

confidence: 99%

Parallel graph algorithms in constant adaptive rounds

Behnezhad

Dhulipala²,

Esfandiari

et al. 2020

Proc. VLDB Endow.

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We study fundamental graph problems such as graph connectivity, minimum spanning forest (MSF), and approximate maximum (weight) matching in a distributed setting. In particular, we focus on the Adaptive Massively Parallel Computation (AMPC) model, which is a theoretical model that captures MapReduce-like computation augmented with a distributed hash table. We show the first AMPC algorithms for all of the studied problems that run in a constant number of rounds and use only O ( n ϵ ) space per machine, where 0 < ϵ < 1. Our results improve both upon the previous results in the AMPC model, as well as the best-known results in the MPC model, which is the theoretical model underpinning many popular distributed computation frameworks, such as MapReduce, Hadoop, Beam, Pregel and Giraph. Finally, we provide an empirical comparison of the algorithms in the MPC and AMPC models in a fault-tolerant distributed computation environment. We empirically evaluate our algorithms on a set of large real-world graphs and show that our AMPC algorithms can achieve improvements in both running time and round-complexity over optimized MPC baselines.

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“…Many computational problems, such as graph problems [2,7,8,9,10,11,13,14,15,20,21,27,30,32,41,44,40,49,51,59,63], clustering [16,18,36,43,65] and submodular function optimization [33,37,48,56], have been studied in this model, with an emphasis on developing algorithms that minimize the number of communication rounds. For example, recently, [46] showed that massively parallel computation can simulate dynamic programming algorithms admitting two properties, i.e.…”

Section: Introductionmentioning

confidence: 99%

On the Hardness of Massively Parallel Computation

Chung

Sun

2020

Proceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures

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We investigate whether there are inherent limits of parallelization in the (randomized) massively parallel computation (MPC) model by comparing it with the (sequential) RAM model. As our main result, we show the existence of hard functions that are essentially not parallelizable in the MPC model. Based on the widely-used random oracle methodology in cryptography with a cryptographic hash function h : {0, 1} n → {0, 1} n computable in time t h , we show that there exists a function that can be computed in time O(T • t h) and space S by a RAM algorithm, but any MPC algorithm with local memory size s < S/c for some c > 1 requires at least Ω(T) 1 rounds to compute the function, even in the average case, for a wide range of parameters n ≤ S ≤ T ≤ 2 n 1/4. Our result is almost optimal in the sense that by taking T to be much larger than t h , e.g., T to be sub-exponential in t h , to compute the function, the round complexity of any MPC algorithm with small local memory size is asymptotically the same (up to a polylogarithmic factor) as the time complexity of the RAM algorithm. Our result is obtained by adapting the so-called compression argument from the data structure lower bounds and cryptography literature to the context of massively parallel computation.

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Round compression for parallel matching algorithms

Cited by 55 publications

References 35 publications

Graph Sparsification for Derandomizing Massively Parallel Computation with Low Space

Graph Sparsification for Derandomizing Massively Parallel Computation with Low Space

Parallel graph algorithms in constant adaptive rounds

On the Hardness of Massively Parallel Computation

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