Deterministic Approximation for Submodular Maximization over a Matroid in Nearly Linear Time

We study the problem of maximizing a non-monotone, non-negative submodular function subject to a matroid constraint. Our approach is based on a novel algorithmic framework of simultaneously constructing two candidate solution sets through greedy search, which enables us to get improved performance bounds by fully exploiting the properties of independence systems. As a byproduct of this framework, we also show that TwinGreedyFast achieves \frac{1}{2p 2}-\epsilon deterministic ratio under a p -set system constraint with the same time complexity. To showcase the practicality of our approach, we empirically evaluated the performance of TwinGreedyFast on two network applications, and observed that it outperforms the state-of-the-art deterministic and randomized algorithms with efficient implementations for our problem.