Constrained Submodular Maximization: Beyond 1/e

TL;DR

This paper introduces a novel algorithm for non-monotone submodular maximization under general constraints, achieving a better approximation ratio of 0.372, surpassing the previous 1/e limit set by earlier methods.

Contribution

It presents the first improvement over the 1/e approximation for this problem by developing a new algorithm with a 0.372 guarantee.

Findings

Achieved a 0.372 approximation ratio for non-monotone submodular maximization.

First algorithm to surpass the 1/e approximation barrier in this setting.

Applicable to maximizing the multilinear extension over down-closed polytopes.

Abstract

In this work, we present a new algorithm for maximizing a non-monotone submodular function subject to a general constraint. Our algorithm finds an approximate fractional solution for maximizing the multilinear extension of the function over a down-closed polytope. The approximation guarantee is 0.372 and it is the first improvement over the 1/e approximation achieved by the unified Continuous Greedy algorithm [Feldman et al., FOCS 2011].