Parallelizing greedy for submodular set function maximization in matroids and beyond

Chekuri, Chandra; Quanrud, Kent

doi:10.1145/3313276.3316406

Cited by 34 publications

(27 citation statements)

References 45 publications

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“…We acknowledge that the query complexity can likely be improved via normalization or estimating an indicator random variable instead. The works of (Chekuri & Quanrud, 2018;Ene et al, 2018b) give constant-factor approximation algorithms with O(log 2 (n)) adaptivity for maximizing nonmonotone submodular functions subject to matroid constraints. Their approaches use multilinear extensions and thus require Ω(nk 2 log 2 (n)) function evaluations to simulate an oracle for ∇f with high enough accuracy.…”

Section: Algorithm Approximiation Adaptivity Queriesmentioning

confidence: 99%

Submodular Maximization with Nearly Optimal Approximation, Adaptivity and Query Complexity

Fahrbach

Mirrokni

Zadimoghaddam

2019

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

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Submodular maximization is a general optimization problem with a wide range of applications in machine learning (e.g., active learning, clustering, and feature selection). In large-scale optimization, the parallel running time of an algorithm is governed by its adaptivity, which measures the number of sequential rounds needed if the algorithm can execute polynomially-many independent oracle queries in parallel. While low adaptivity is ideal, it is not sufficient for an algorithm to be efficient in practice-there are many applications of distributed submodular optimization where the number of function evaluations becomes prohibitively expensive. Motivated by these applications, we study the adaptivity and query complexity of submodular maximization. In this paper, we give the first constant-factor approximation algorithm for maximizing a nonmonotone submodular function subject to a cardinality constraint k that runs in O(log(n)) adaptive rounds and makes O(n log(k)) oracle queries in expectation. In our empirical study, we use three real-world applications to compare our algorithm with several benchmarks for non-monotone submodular maximization. The results demonstrate that our algorithm finds competitive solutions using significantly fewer rounds and queries.

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Section: Algorithm Approximiation Adaptivity Queriesmentioning

confidence: 99%

Submodular Maximization with Nearly Optimal Approximation, Adaptivity and Query Complexity

Fahrbach

Mirrokni

Zadimoghaddam

2019

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

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“…We need the following Lemma in our analysis. The proof idea follows from [BV14] and it appears in [CQ19,BRS19b]. It has some minor difference with previous work and we provide a proof for completeness.…”

Section: Amplification Via Accelerated Continuous Greedymentioning

confidence: 99%

“…In each iteration, we use the above combinatorial algorithm to find the direction of improvement of the multi-linear extension. We remark a similar amplifying procedure has been used in the previous work on adaptive submodular maximization [CQ19,BRS19b].…”

Section: Technical Overviewmentioning

confidence: 99%

On the Complexity of Dynamic Submodular Maximization

Chen¹,

Peng²

2021

Preprint

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We study dynamic algorithms for the problem of maximizing a monotone submodular function over a stream of n insertions and deletions. We show that any algorithm that maintains a (0.5 + ǫ)-approximate solution under a cardinality constraint, for any constant ǫ > 0, must have an amortized query complexity that is polynomial in n. Moreover, a linear amortized query complexity is needed in order to maintain a 0.584-approximate solution. This is in sharp contrast with recent dynamic algorithms of [LMNF + 20, Mon20] that achieve (0.5 − ǫ)-approximation with a polylog(n) amortized query complexity.On the positive side, when the stream is insertion-only, we present efficient algorithms for the problem under a cardinality constraint and under a matroid constraint with approximation guarantee 1 − 1/e − ǫ and amortized query complexities O(log(k/ǫ)/ǫ 2 ) and k O(1/ǫ 2 ) log n, respectively, where k denotes the cardinality parameter or the rank of the matroid.

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“…Subsequently, Balkanski et al (2019), Ene and Nguyen (2019) and Fahrbach et al (2019) independently designed two 1 − 1/e − ε-approximation algorithms through using different methods and techniques, both requiring the O((log(n))) adaptivity rounds and the O(n) oracle queries in expectation. Later, submodular maximization with matroid constraints Chekuri and Quanrud 2019b), submodular maximization subject to packing constraints Chekuri and Quanrud 2019a) and the submodular cover problem (Agarwal et al 2019) have been studied in the adaptive complexity model.…”

Section: Introductionmentioning

confidence: 99%

Approximation guarantees for parallelized maximization of monotone non-submodular function with a cardinality constraint

Cui

Guo

et al. 2021

J Comb Optim

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Emerging applications in machine learning have imposed the problem of monotone non-submodular maximization subject to a cardinality constraint. Meanwhile, parallelism is prevalent for large-scale optimization problems in bigdata scenario while adaptive complexity is an important measurement of parallelism since it quantifies the number of sequential rounds by which the multiple independent functions can be evaluated in parallel. For a monotone non-submodular function and a cardinality constraint, this paper devises an adaptive algorithm for maximizing the function value with the cardinality constraint through employing the generic submodularity ratio γ to connect the monotone set function with submodularity. The algorithm achieves an approximation ratio of 1 − e −γ 2 − ε and consumes O(log(n/η)/ε 2 ) adaptive rounds and O(n log log(k)/ε 3 ) oracle queries in expectation. Furthermore, when γ = 1, the

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Parallelizing greedy for submodular set function maximization in matroids and beyond

Cited by 34 publications

References 45 publications

Submodular Maximization with Nearly Optimal Approximation, Adaptivity and Query Complexity

Submodular Maximization with Nearly Optimal Approximation, Adaptivity and Query Complexity

On the Complexity of Dynamic Submodular Maximization

Approximation guarantees for parallelized maximization of monotone non-submodular function with a cardinality constraint

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