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Submodular Maximization Through Barrier Functions

Ashwinkumar Badanidiyuru,Amin Karbasi,Ehsan Kazemi,J. Vondrák

Published 2020 in Neural Information Processing Systems

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.

PUBLICATION RECORD

  • Publication year

    2020

  • Venue

    Neural Information Processing Systems

  • Publication date

    2020-02-01

  • Fields of study

    Mathematics, Computer Science

  • Identifiers
    arXiv 2002.03523
  • External record

    Open on Semantic Scholar

  • Source metadata

    Semantic Scholar

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