Streaming Submodular Maximization under a $k$-Set System Constraint

• URL: http://arxiv.org/abs/2002.03352v1
• Date: Sun, 9 Feb 2020 12:32:14 GMT
• Title: Streaming Submodular Maximization under a $k$-Set System Constraint
• Authors: Ran Haba, Ehsan Kazemi, Moran Feldman and Amin Karbasi
• Abstract summary: We propose a novel framework that converts streaming for monotone submodular into streaming for non-monotone submodular. We also propose the first algorithm for monotone submodular streaming subject to $k$ible $k$-set system constraints.
• Score: 42.31117997337689
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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