Streaming submodular maximization under a k-set system constraint

In this paper, we propose a novel framework that converts streaming algorithms for monotone submodular maximization into streaming algorithms for non-monotone submodular maximization. This reduction readily leads to the currently tightest deterministic approximation ratio for sub modular maximization subject to a k-matchoid constraint. Moreover, we propose the first stream ing algorithm for monotone submodular maxi mization subject to k-extendible and k-set system constraints. Together with our proposed reduction, we obtain O(k log k) and O(k 2 log k) approxima tion ratio for submodular maximization subject to the above constraints, respectively. We exten sively evaluate the empirical performance of our algorithm against the existing work in a series of experiments including finding the maximum independent set in randomly generated graphs, maximizing linear functions over social networks, movie recommendation, Yelp location summa rization, and Twitter data summarization.