A primal-dual algorithm for monotone submodular maximization - Chakrabarty, Deeparnab; Coté, Luc (Operations research letters, 2026)
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.