A primal-dual algorithm for monotone submodular maximization

In this paper we design and analyze a new approximation algorithm for the classic discrete optimization problem of maximizing a monotone submodular function subject to a cardinality constraint. Our algorithm is based on the primal-dual schema and achieves the optimal factor of (1−1/e). While greedy...

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Bibliographic Details
Published in:	Operations research letters Vol. 65; p. 107387
Main Authors:	Chakrabarty, Deeparnab, Coté, Luc
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 01.03.2026
Subjects:	Primal-dual algorithms Submodular functions Submodular functions Primal-dual algorithms
ISSN:	0167-6377
Online Access:	Get full text
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Summary:	In this paper we design and analyze a new approximation algorithm for the classic discrete optimization problem of maximizing a monotone submodular function subject to a cardinality constraint. Our algorithm is based on the primal-dual schema and achieves the optimal factor of (1−1/e). While greedy algorithms have been known to achieve this approximation factor, our algorithms also provide a dual certificate which upper bounds the optimum value of any instance. This certificate can be used to certify instance-wise guarantees potentially much better than the worst-case (1−1/e) approximation factor.
ISSN:	0167-6377
DOI:	10.1016/j.orl.2025.107387