Streaming Submodular Maximization under a $k$-Set System Constraint
This work addresses optimization challenges in streaming data for applications like graph analysis and summarization, offering incremental improvements in approximation algorithms.
The paper tackles the problem of streaming submodular maximization under k-set system constraints by proposing a novel framework that converts streaming algorithms for monotone to non-monotone cases, achieving the tightest deterministic approximation ratios for k-matchoid constraints and first streaming algorithms for k-extendible and k-set system constraints with O(k log k) and O(k^2 log k) ratios, respectively.
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 submodular maximization subject to a $k$-matchoid constraint. Moreover, we propose the first streaming algorithm for monotone submodular maximization subject to $k$-extendible and $k$-set system constraints. Together with our proposed reduction, we obtain $O(k\log k)$ and $O(k^2\log k)$ approximation ratio for submodular 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.