Deterministic (1/2 + {\epsilon})-Approximation for Submodular Maximization over a Matroid

TL;DR

This paper introduces a deterministic algorithm that surpasses the 1/2 approximation barrier for maximizing monotone submodular functions under matroid constraints, marking a significant advancement over classical methods.

Contribution

The paper presents the first deterministic algorithm achieving better than 1/2 approximation for submodular maximization under matroids, improving upon classical greedy approaches.

Findings

Achieves (1/2 + ε)-approximation ratio.

First deterministic algorithm to beat 1/2 ratio.

Improves theoretical bounds for submodular maximization.

Abstract

We study the problem of maximizing a monotone submodular function subject to a matroid constraint and present a deterministic algorithm that achieves (1/2 + {\epsilon})-approximation for the problem. This algorithm is the first deterministic algorithm known to improve over the 1/2-approximation ratio of the classical greedy algorithm proved by Nemhauser, Wolsely and Fisher in 1978.