A New Framework for Distributed Submodular Maximization

Barbosa, Rafael da Ponte; Ene, Alina; Nguyêݱn, Huy L.; Ward, Justin

doi:10.1109/focs.2016.74

Cited by 36 publications

(10 citation statements)

References 25 publications

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“…Motivated by the growing data size, extensive effort has been made to develop distributed algorithms for SMCC using the MapReduce (MR) framework, e.g. Mirzasoleiman et al (2013); Mirrokni and Zadimoghaddam (2015); Barbosa et al (2016); Kazemi et al (2021) (see Table 1). The proposed distributed algorithms of Barbosa et al (2015) and Barbosa et al (2016) provide a way to utilize a given centralized, approximation algorithm ALG in a distributed setting, where ALG is executed on the distributed data over a constant number of MR rounds to yield a constant approximation.…”

Section: Introductionmentioning

confidence: 99%

“…Mirzasoleiman et al (2013); Mirrokni and Zadimoghaddam (2015); Barbosa et al (2016); Kazemi et al (2021) (see Table 1). The proposed distributed algorithms of Barbosa et al (2015) and Barbosa et al (2016) provide a way to utilize a given centralized, approximation algorithm ALG in a distributed setting, where ALG is executed on the distributed data over a constant number of MR rounds to yield a constant approximation. In order for their theoretical guarantees to hold, ALG must satisfy a consistency property (formally defined in Property 1).…”

Section: Introductionmentioning

confidence: 99%

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DASH: A Distributed and Parallelizable Algorithm for Size-Constrained Submodular Maximization

Dey

Chen

Kuhnle

2023

AAAI

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MapReduce (MR) algorithms for maximizing monotone, submodular functions subject to a cardinality constraint (SMCC) are currently restricted to the use of the linear-adaptive (non-parallelizable) algorithm GREEDY. Low-adaptive algorithms do not satisfy the requirements of these distributed MR frameworks, thereby limiting their performance. We study the SMCC problem in a distributed setting and propose the first MR algorithms with sublinear adaptive complexity. Our algorithms, R-DASH, T-DASH and G-DASH provide 0.316 - ε, 3/8 - ε , and (1 - 1/e - ε) approximation ratios, respectively, with nearly optimal adaptive complexity and nearly linear time complexity. Additionally, we provide a framework to increase, under some mild assumptions, the maximum permissible cardinality constraint from O( n / ℓ^2) of prior MR algorithms to O( n / ℓ ), where n is the data size and ℓ is the number of machines; under a stronger condition on the objective function, we increase the maximum constraint value to n. Finally, we provide empirical evidence to demonstrate that our sublinear-adaptive, distributed algorithms provide orders of magnitude faster runtime compared to current state-of-the-art distributed algorithms.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

DASH: A Distributed and Parallelizable Algorithm for Size-Constrained Submodular Maximization

Dey

Chen

Kuhnle

2023

AAAI

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“…From a more practical perspective, submodular maximization problems have found uses in social networks [52,60], vision [12,56], machine learning [64,65,66,72,73] and many other areas (the reader is referred, for example, to a comprehensive survey by Bach [5]). Submodular maximization has also been studied in various computational models, such as online and secretary (random arrival) settings [8,15,19,45], streaming [2,21,41,44,59,71], parallel computation [6,7,23,24] and distributed computing [74,83]. Some works also took a game theoretic perspective on submodular optimization [3,32,77].…”

Section: Introductionmentioning

confidence: 99%

Constrained Submodular Maximization via a Nonsymmetric Technique

Buchbinder

Feldman

2019

Mathematics of OR

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The study of combinatorial optimization problems with a submodular objective has attracted much attention in recent years. Such problems are important in both theory and practice because their objective functions are very general. Obtaining further improvements for many submodular maximization problems boils down to finding better algorithms for optimizing a relaxation of them known as the multilinear extension.In this work we present an algorithm for optimizing the multilinear relaxation whose guarantee improves over the guarantee of the best previous algorithm (which was given by Ene and Nguyen (2016)). Moreover, our algorithm is based on a new technique which is, arguably, simpler and more natural for the problem at hand. In a nutshell, previous algorithms for this problem rely on symmetry properties which are natural only in the absence of a constraint. Our technique avoids the need to resort to such properties, and thus, seems to be a better fit for constrained problems.

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“…Recent applications of submodular function maximization to large data sets, and technological trends, have motivated new directions of research. These include the study of faster algorithms in the sequential model of computation [2,34,19,35,27], algorithms in distributed setting [33,29,32,8,9,30], and algorithms in the streaming setting [3,14,18]. Barbosa et al [9] developed a general technique to obtain a constant round algorithm in the MapReduce model of computation that gets arbitrarily close to the approximation achievable in the sequential setting.…”

Section: Introductionmentioning

confidence: 99%

Submodular Function Maximization in Parallel via the Multilinear Relaxation

Chekuri

Quanrud

2019

Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms

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Balkanski and Singer [4] recently initiated the study of adaptivity (or parallelism) for constrained submodular function maximization, and studied the setting of a cardinality constraint. Subsequent improvements for this problem by Balkanski, Rubinstein, and Singer [6] and Ene and Nguyen [21] resulted in a near-optimal (1−1/e−ǫ)-approximation in O(log n/ǫ 2 ) rounds of adaptivity. Partly motivated by the goal of extending these results to more general constraints, we describe parallel algorithms for approximately maximizing the multilinear relaxation of a monotone submodular function subject to packing constraints. Formally our problem is to maximize F (x) over x ∈ [0, 1] n subject to Ax ≤ 1 where F is the multilinear relaxation of a monotone submodular function. Our algorithm achieves a near-optimal (1 − 1/e − ǫ)-approximation in O(log 2 m log n/ǫ 4 ) rounds where n is the cardinality of the ground set and m is the number of packing constraints. For many constraints of interest, the resulting fractional solution can be rounded via known randomized rounding schemes that are oblivious to the specific submodular function. We thus derive randomized algorithms with poly-logarithmic adaptivity for a number of constraints including partition and laminar matroids, matchings, knapsack constraints, and their intersections.Our algorithm takes a continuous view point and combines several ideas ranging from the continuous greedy algorithm of [38,13], its adaptation to the MWU framework for packing constraints [19], and parallel algorithms for packing LPs [31,41]. For the basic setting of cardinality constraints, this viewpoint gives rise to an alternative, simple to understand algorithm that matches recent results [6,21]. Our algorithm to solve the multilinear relaxation is deterministic if it is given access to a value oracle for the multilinear extension and its gradient; this is possible in some interesting cases such as the coverage function of an explicitly given set system.

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A New Framework for Distributed Submodular Maximization

Cited by 36 publications

References 25 publications

DASH: A Distributed and Parallelizable Algorithm for Size-Constrained Submodular Maximization

DASH: A Distributed and Parallelizable Algorithm for Size-Constrained Submodular Maximization

Constrained Submodular Maximization via a Nonsymmetric Technique

Submodular Function Maximization in Parallel via the Multilinear Relaxation

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