Streaming Submodular Maximization under a k-Set System Constraint

In this paper, we propose a novel frame work that converts streaming algorithms for monotone sub modular maximization into streaming algorithms for non-monotone sub modular maximization. This reduction readily leads to the currently tightest deterministic approximation ratio for sub modular maximization subject to a k-match oid constraint. Moreover, we propose the first streaming algorithm for monotone sub modular maximization subject to k-extendible and k-set system constraints. Together with our proposed reduction, we obtain O(k log k) and O(k²log k) approximation ratio for sub modular maximization subject to the above constraints, respectively. We extensively 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 summarization, and Twitter data summarization.