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].
@article{arxiv.1608.03611,
title = {Constrained Submodular Maximization: Beyond 1/e},
author = {Alina Ene and Huy L. Nguyen},
journal= {arXiv preprint arXiv:1608.03611},
year = {2016}
}