Submodular Maximization Through Barrier Functions

• URL: http://arxiv.org/abs/2002.03523v1
• Date: Mon, 10 Feb 2020 03:32:49 GMT
• Title: Submodular Maximization Through Barrier Functions
• Authors: Ashwinkumar Badanidiyuru and Amin Karbasi and Ehsan Kazemi and Jan Vondrak
• Abstract summary: We introduce a novel technique for constrained submodular, inspired by barrier functions in continuous optimization. We extensively evaluate our proposed algorithm over several real-world applications.
• Score: 32.41824379833395
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we introduce a novel technique for constrained submodular maximization, inspired by barrier functions in continuous optimization. This connection not only improves the running time for constrained submodular maximization but also provides the state of the art guarantee. More precisely, for maximizing a monotone submodular function subject to the combination of a $k$-matchoid and $\ell$-knapsack constraint (for $\ell\leq k$), we propose a potential function that can be approximately minimized. Once we minimize the potential function up to an $\epsilon$ error it is guaranteed that we have found a feasible set with a $2(k+1+\epsilon)$-approximation factor which can indeed be further improved to $(k+1+\epsilon)$ by an enumeration technique. We extensively evaluate the performance of our proposed algorithm over several real-world applications, including a movie recommendation system, summarization tasks for YouTube videos, Twitter feeds and Yelp business locations, and a set cover problem.

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