Streaming Algorithms for Submodular Function Maximization

Chekuri, Chandra; Gupta, Shalmoli; Quanrud, Kent

doi:10.1007/978-3-662-47672-7_26

Cited by 82 publications

(140 citation statements)

References 48 publications

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“…Our hardness result matches the competitive ratio by [CK14,CGQ15]. Randomized Algorithms on Partition Matroids.…”

Section: K-uniformsupporting

confidence: 74%

“…We propose a deterministic monotone algorithm (Section 3) that is at least 0.2959-competitive for monotone submodular functions, improving the previous ratio of 0.25 [BFS15,CK14,CGQ15]. As k tends to infinity, our competitive ratio approaches 1 α∞ ≈ 0.3178 (from below), where α ∞ is the unique root of α = e α−2 that is greater than 1.…”

Section: K-uniformmentioning

confidence: 93%

“…Observe that essentially the same algorithm is given in [CK14,CGQ15]. However, as we wish to emphasize monotonicity and will also need to generalize the techniques in Section 8, we give a proof here.…”

Section: Monotone Algorithm With General Matroid Constraintmentioning

confidence: 99%

“…Streaming Model. Chakrabarti and Kale [CK14] and Chekuri et al [CGQ15] considered streaming version of this problem in which the algorithm has limited memory. They consider even more general independent systems than matroids, and their algorithms for the case of matroids can be interpreted as an online algorithm with free disposal that is 0.25-competitive.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Online Submodular Maximization with Free Disposal: Randomization Beats ¼ for Partition Matroids

Chan¹,

Huang²,

Jiang³

et al. 2017

Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms

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We study the online submodular maximization problem with free disposal under a matroid constraint. Elements from some ground set arrive one by one in rounds, and the algorithm maintains a feasible set that is independent in the underlying matroid. In each round when a new element arrives, the algorithm may accept the new element into its feasible set and possibly remove elements from it, provided that the resulting set is still independent. The goal is to maximize the value of the final feasible set under some monotone submodular function, to which the algorithm has oracle access.For k-uniform matroids, we give a deterministic algorithm with competitive ratio at least 0.2959, and the ratio approaches . We also show that our algorithm is optimal among a class of deterministic monotone algorithms that accept a new arriving element only if the objective is strictly increased.Further, we prove that no deterministic monotone algorithm can be strictly better than 0.25-competitive even for partition matroids, the most modest generalization of k-uniform matroids, matching the competitive ratio by Chakrabarti and Kale (IPCO 2014) and Chekuri et al. (ICALP 2015). Interestingly, we show that randomized algorithms are strictly more powerful by giving a (non-monotone) randomized algorithm for partition matroids with ratio 1 α∞ ≈ 0.3178.Finally, our techniques can be extended to a more general problem that generalizes both the online submodular maximization problem and the online bipartite matching problem with free disposal. Using the techniques developed in this paper, we give constantcompetitive algorithms for the submodular online bipartite matching problem.

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“…Our hardness result matches the competitive ratio by [CK14,CGQ15]. Randomized Algorithms on Partition Matroids.…”

Section: K-uniformsupporting

confidence: 74%

Section: K-uniformmentioning

confidence: 93%

Section: Monotone Algorithm With General Matroid Constraintmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Online Submodular Maximization with Free Disposal: Randomization Beats ¼ for Partition Matroids

Chan¹,

Huang²,

Jiang³

et al. 2017

Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms

View full text Add to dashboard Cite

show abstract

“…Since sublinear competitive ratio is not possible in general with adversarial order, they consider a relaxed model where we are allowed to drop items (preemption) and give constant-competitive algorithms. Submodular maximization has also been studied in the streaming setting, where we have space constraints but are again allowed to drop items [6,15,16].…”

Section: Further Related Workmentioning

confidence: 99%

Combinatorial Prophet Inequalities

Rubinstein¹,

Singla²

2017

Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms

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We introduce a novel framework of Prophet Inequalities for combinatorial valuation functions. For a (non-monotone) submodular objective function over an arbitrary matroid feasibility constraint, we give an O(1)-competitive algorithm. For a monotone subadditive objective function over an arbitrary downwardclosed feasibility constraint, we give an O(log n log 2 r)-competitive algorithm (where r is the cardinality of the largest feasible subset).Inspired by the proof of our subadditive prophet inequality, we also obtain an O(log n · log 2 r)-competitive algorithm for the Secretary Problem with a monotone subadditive objective function subject to an arbitrary downward-closed feasibility constraint. Even for the special case of a cardinality feasibility constraint, our algorithm circumvents an Ω( √ n) lower bound by Bateni, Hajiaghayi, and Zadimoghaddam [10] in a restricted query model.En route to our submodular prophet inequality, we prove a technical result of independent interest: we show a variant of the Correlation Gap Lemma [14, 1] for nonmonotone submodular functions.

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Improved Streaming Algorithms for Maximizing Monotone Submodular Functions Under a Knapsack Constraint

Huang

Kakimura

2019

Lecture Notes in Computer Science

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In this paper, we consider the problem of maximizing a monotone submodular function subject to a knapsack constraint in a streaming setting. In such a setting, elements arrive sequentially and at any point in time, and the algorithm can store only a small fraction of the elements that have arrived so far. For the special case that all elements have unit sizes (i.e., the cardinality-constraint case), one can find a (0.5 − ε)-approximate solution in O(Kε −1 ) space, where K is the knapsack capacity (Badanidiyuru et al. KDD 2014). The approximation ratio is recently shown to be optimal (Feldman et al. STOC 2020). In this work, we propose a (0.4 − ε)-approximation algorithm for the knapsack-constrained problem, using space that is a polynomial of K and ε. This improves on the previous best ratio of 0.363 − ε with space of the same order. Our algorithm is based on a careful combination of various ideas to transform multiple-pass streaming algorithms into a single-pass one.

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Streaming Algorithms for Submodular Function Maximization

Cited by 82 publications

References 48 publications

Online Submodular Maximization with Free Disposal: Randomization Beats ¼ for Partition Matroids

Online Submodular Maximization with Free Disposal: Randomization Beats ¼ for Partition Matroids

Combinatorial Prophet Inequalities

Improved Streaming Algorithms for Maximizing Monotone Submodular Functions Under a Knapsack Constraint

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