A deterministic approximation algorithm is presented for the maximization of non-monotone submodular functions over a ground set of size $n$ subject to cardinality constraint $k$; the algorithm is based upon the idea of interlacing two greedy procedures. The algorithm uses interlaced, thresholded greedy procedures to obtain tight ratio $1/4 - \epsilon$ in $O \left( \frac{n}{\epsilon} \log \left( \frac{k}{\epsilon} \right) \right)$ queries of the objective function, which improves upon both the ratio and the quadratic time complexity of the previously fastest deterministic algorithm for this problem. The algorithm is validated in the context of two applications of non-monotone submodular maximization, on which it outperforms the fastest deterministic and randomized algorithms in prior literature.

In this paper, the authors study the problem of maximizing a non-monotone submodular function subject to a cardinality constraint and present a deterministic algorithm that achieves (1/4 - \epsilon)-approximation for the problem. Their fastest algorithm makes O(n / \epsilon \log(n / \epsilon)) queries to the oracle. While Buchbinder et al. (2015) have designed a randomized algorithm with better approximation factor and time complexity, the algorithm presented in this paper is deterministic. Although I believe deterministic algorithms which guarantee the performance in the worst-case scenarios are interesting for many researchers in the field, the contribution level of this paper is borderline. Also, I checked almost all the proofs in this paper.

This is a nice contribution on deterministic (non-monotone) submodular maximization subject to a size constraint. All the reviewers liked the paper. Please add the missing references to the final version.

A deterministic approximation algorithm is presented for the maximization of non-monotone submodular functions over a ground set of size n subject to cardinality constraint k; the algorithm is based upon the idea of interlacing two greedy procedures. The algorithm uses interlaced, thresholded greedy procedures to obtain tight ratio 1/4 - \epsilon in O \left( \frac{n}{\epsilon} \log \left( \frac{k}{\epsilon} \right) \right) queries of the objective function, which improves upon both the ratio and the quadratic time complexity of the previously fastest deterministic algorithm for this problem. The algorithm is validated in the context of two applications of non-monotone submodular maximization, on which it outperforms the fastest deterministic and randomized algorithms in prior literature.

A deterministic approximation algorithm is presented for the maximization of non-monotone submodular functions over a ground set of size $n$ subject to cardinality constraint $k$; the algorithm is based upon the idea of interlacing two greedy procedures. The algorithm uses interlaced, thresholded greedy procedures to obtain tight ratio $1/4 - \epsilon$ in $O \left( \frac{n}{\epsilon} \log \left( \frac{k}{\epsilon} \right) \right)$ queries of the objective function, which improves upon both the ratio and the quadratic time complexity of the previously fastest deterministic algorithm for this problem. The algorithm is validated in the context of two applications of non-monotone submodular maximization, on which it outperforms the fastest deterministic and randomized algorithms in prior literature. Papers published at the Neural Information Processing Systems Conference.