An Efficient Framework for Balancing Submodularity and Cost

Nikolakaki, Sofia Maria; Ene, Alina; Terzi, Evimaria

doi:10.48550/arxiv.2002.07782

Cited by 2 publications

(6 citation statements)

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“…The properties of the distorted greedy algorithm are summarized using the following theorem. Notably, an independent study for the general matroid constrained regularized submodular maximization is available [19] . Theorem 1 Algorithm 1 obtains a weak 0:5approximation for maximizing regularized submodular functions under a partition matroid constraint.…”

Section: Discussionmentioning

confidence: 99%

“…[17], which considered the setting with a non-monotone submodular utility and obtained a weak 1=e-approximation. References [18][19][20] can be used as a reference for optimizing the regularized submodular models.…”

Section: Related Workmentioning

confidence: 99%

“…References [34][35][36] summarized the submodular maximization under a random order. Additionally, streaming algorithms were originally developed for the regularized problems [13,19,37] .…”

Section: Related Workmentioning

confidence: 99%

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A Note on Maximizing Regularized Submodular Functions Under Streaming

Gong,

Meng,

Yang

et al. 2023

Tsinghua Sci. Technol.

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Recent progress in maximizing submodular functions with a cardinality constraint through centralized and streaming modes has demonstrated a wide range of applications and also developed comprehensive theoretical guarantees. The submodularity was investigated to capture the diversity and representativeness of the utilities, and the monotonicity has the advantage of improving the coverage. Regularized submodular optimization models were developed in the latest studies (such as a house on fire), which aimed to sieve subsets with constraints to optimize regularized utilities. This study is motivated by the setting in which the input stream is partitioned into several disjoint parts, and each part has a limited size constraint. A first threshold-based bicriteria .1=3; 2=3/-approximation for the problem is provided.

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Section: Discussionmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

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A Note on Maximizing Regularized Submodular Functions Under Streaming

Gong,

Meng,

Yang

et al. 2023

Tsinghua Sci. Technol.

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“…In order to estimate the value f (x * ), we take the means of the maximum singleton value m = max e∈E f (χ e ) instead which inspired by the ideas of Badanidiyuru et al [13] and Ene [1]. Also, form their discussion above the OPT, we can ensure that m ≤ OP T ≤ km.…”

Section: Algorithm 1 Streaming Algorithm For G-c On the Integer Latticementioning

confidence: 99%

“…In many practical scenarios, it is necessary to strike a balance between the benefits of selecting V , quantified by the function g(V ), and the associated cost denoted as c(V ). To cater to these application domains, Nikolakaki et al [1] characterized the team formation problem as the following maximization problem model:…”

Section: Introductionmentioning

confidence: 99%

Streaming Algorithms for Maximization of a Non-submodular Function with a Cardinality Constraint on the Integer Lattice

Tan

Sun

et al. 2022

Parallel and Distributed Computing, Applications and Technologies

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Team formation problem is a very important problem in the labor market, and it is proved to be NP-hard. In this paper, we design an efficient bicriteria streaming algorithms to construct a balance between gain and cost in a team formation problem with cardinality constraint on the integer lattice. To solve this problem, we establish a model for maximizing the difference between a nonnegative normalized monotone submodule function and a nonnegative linear function. Further, we discuss the case where the first function is α-weakly submodular. Combining the lattice binary search with the threshold method, we present an online algorithm called bicriteria streaming algorithms. Meanwhile, we give detailed analysis for both of these models.

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An Efficient Framework for Balancing Submodularity and Cost

Cited by 2 publications

References 0 publications

A Note on Maximizing Regularized Submodular Functions Under Streaming

A Note on Maximizing Regularized Submodular Functions Under Streaming

Streaming Algorithms for Maximization of a Non-submodular Function with a Cardinality Constraint on the Integer Lattice

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