Streaming Submodular Matching Meets the Primal-Dual Method

Levin, Roie; Wajc, David

doi:10.1137/1.9781611976465.114

Cited by 18 publications

(20 citation statements)

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“…Using this instance, we are able to upper bound the approximation ratio that can be obtained using a streaming algorithm for the problem of maximizing a monotone submodular function subject to a bipartite matching constraint. Our upper bound improves over the previously best known impossibility of 0.52 due to Levin and Wajc [LW21] assuming that the graph can contain parallel edges (which are distinct elements from the point of view of the submodular objective function); the hardness of [LW21] applies even when this is not the case.…”

Section: Introductionmentioning

confidence: 61%

Streaming Submodular Maximization under Matroid Constraints

Feldman¹,

Liu²,

Norouzi-Fard³

et al. 2021

Preprint

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Recent progress in (semi-)streaming algorithms for monotone submodular function maximization has led to tight results for a simple cardinality constraint. However, current techniques fail to give a similar understanding for natural generalizations such as matroid and matching constraints. This paper aims at closing this gap. For a single matroid of rank k (i.e., any solution has cardinality at most k), our main results are:

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Section: Introductionmentioning

confidence: 61%

Streaming Submodular Maximization under Matroid Constraints

Feldman¹,

Liu²,

Norouzi-Fard³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…They also proved, conditioned on some complexity-theoretic assumption, a lower bound of 1.914 on the approximation ratio that can be obtained by a semi-streaming algorithm for the problem. Our final result improves over this upper bound and is independent of any complexitytheoretic assumption, but does assume that the graph can contain parallel edges (which are distinct elements from the point of view of the submodular objective function); the hardness of [25] applies even when this is not the case.…”

Section: Introductionmentioning

confidence: 70%

“…Such algorithms are known as semi-streaming algorithms. Recently, Levin and Wajc [25] described a semi-streaming algorithm for maximizing a monotone submodular function subject to a bipartite matching constraint which improves over the state-of-the-art for general SMkM with a monotone objective function. They also proved, conditioned on some complexity-theoretic assumption, a lower bound of 1.914 on the approximation ratio that can be obtained by a semi-streaming algorithm for the problem.…”

Section: Introductionmentioning

confidence: 99%

Submodular Maximization Subject to Matroid Intersection on the Fly

Feldman¹,

Norouzi-Fard²,

Svensson³

et al. 2022

Preprint

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Despite a surge of interest in submodular maximization in the data stream model, there remain significant gaps in our knowledge about what can be achieved in this setting, especially when dealing with multiple constraints. In this work, we nearly close several basic gaps in submodular maximization subject to k matroid constraints in the data stream model. We present a new hardness result showing that super polynomial memory in k is needed to obtain an o( k /log k)-approximation. This implies near optimality of prior algorithms. For the same setting, we show that one can nevertheless obtain a constant-factor approximation by maintaining a set of elements whose size is independent of the stream size. Finally, for bipartite matching constraints, a well-known special case of matroid intersection, we present a new technique to obtain hardness bounds that are significantly stronger than those obtained with prior approaches. Prior results left it open whether a 2-approximation may exist in this setting, and only a complexity-theoretic hardness of 1.91 was known. We prove an unconditional hardness of 2.69.

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“…Knowing whether it is possible to achieve a better approximation ratio is a major open question in the field of streaming algorithms. For weighted matchings an approximation ratio of 2 + ε can be achieved [12,18,19]. For weighted b-matchings the approximation ratio 2 + ε can also be attained [14].…”

Section: Related Workmentioning

confidence: 99%

Maximum Weight b-Matchings in Random-Order Streams

Huang¹,

Sellier²

2022

Preprint

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We consider the maximum weight b-matching problem in the random-order semi-streaming model. Assuming all weights are small integers drawn from [1, W ], we present a 2 − 1 2W + ε approximation algorithm, using a memory of O(max (|MG|, n) • poly(log(m), W, 1/ε)), where |MG| denotes the cardinality of the optimal matching. Our result generalizes that of Bernstein [3], which achieves a 3/2 + ε approximation for the maximum cardinality simple matching. When W is small, our result also improves upon that of Gamlath et al. [11], which obtains a 2 − δ approximation (for some small constant δ ∼ 10 −17 ) for the maximum weight simple matching. In particular, for the weighted b-matching problem, ours is the first result beating the approximation ratio of 2. Our technique hinges on a generalized weighted version of edge-degree constrained subgraphs, originally developed by Bernstein and Stein [5]. Such a subgraph has bounded vertex degree (hence uses only a small number of edges), and can be easily computed. The fact that it contains a 2 − 1 2W + ε approximation of the maximum weight matching is proved using the classical Kőnig-Egerváry's duality theorem.

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Streaming Submodular Matching Meets the Primal-Dual Method

Cited by 18 publications

References 0 publications

Streaming Submodular Maximization under Matroid Constraints

Streaming Submodular Maximization under Matroid Constraints

Submodular Maximization Subject to Matroid Intersection on the Fly

Maximum Weight b-Matchings in Random-Order Streams

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