A new greedy strategy for maximizing monotone submodular function under a cardinality constraint

In this paper, we study the problem of maximizing a monotone non-decreasing submodular function f : 2 Ω → R + subject to a cardinality constraint, i.e., max { f ( A ) : | A | ≤ k , A ⊆ Ω } . We propose a deterministic algorithm based on a new greedy strategy for solving this problem. We prove that w...

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Bibliographic Details
Published in:Journal of global optimization Vol. 83; no. 2; pp. 235 - 247
Main Authors: Lu, Cheng, Yang, Wenguo, Gao, Suixiang
Format: Journal Article
Language:English
Published: New York Springer US 01.06.2022
Springer
Springer Nature B.V
Subjects:
Algorithms
Computer Science
Greedy algorithms
Mathematics
Mathematics and Statistics
Maximization
Operations Research/Decision Theory
Optimization
Real Functions
Submodular Maximization
Greedy Algorithm
Cardinality Constraint
Curvature
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary:In this paper, we study the problem of maximizing a monotone non-decreasing submodular function f : 2 Ω → R + subject to a cardinality constraint, i.e., max { f ( A ) : | A | ≤ k , A ⊆ Ω } . We propose a deterministic algorithm based on a new greedy strategy for solving this problem. We prove that when the objective function f satisfies certain assumptions, the algorithm we propose can return a 1 - κ f ( 1 - 1 k ) k approximate solution with O ( kn ) value oracle queries, where κ f is the curvature of the monotone submodular function f . We also show that our algorithm outperforms the traditional greedy algorithm in some cases. Furthermore, we demonstrate how to implement our algorithm in practice.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-021-01103-1