A Note On Deterministic Submodular Maximization With Bounded Curvature

TL;DR

This paper discusses how recent advances enable a deterministic approximation algorithm for maximizing submodular functions with bounded curvature under matroid constraints, improving theoretical guarantees.

Contribution

It extends recent results to develop a deterministic algorithm achieving near-optimal approximation ratios for submodular maximization with curvature.

Findings

Deterministic algorithm with approximation ratio close to (1 - curvature/e)

Applicable to submodular functions with bounded curvature under matroid constraints

Builds on recent theoretical breakthroughs in submodular optimization

Abstract

We show that the recent breakthrough result of [Buchbinder and Feldman, FOCS'24] could further lead to a deterministic $(1-\kappa_{f}/e-\varepsilon)$-approximate algorithm for maximizing a submodular function with curvature $\kappa_{f}$ under matroid constraint.