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Robust Monotone Submodular Function Maximization

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Integer Programming and Combinatorial Optimization (IPCO 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9682))

Abstract

We consider a robust formulation, introduced by Krause et al. (2008), of the classic cardinality constrained monotone submodular function maximization problem, and give the first constant factor approximation results. The robustness considered is w.r.t. adversarial removal of a given number of elements from the chosen set. In particular, for the fundamental case of single element removal, we show that one can approximate the problem up to a factor \((1-1/e)-\epsilon \) by making \(O(n^{\frac{1}{\epsilon }})\) queries, for arbitrary \(\epsilon >0\). The ideas are also extended to more general settings.

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Authors and Affiliations

  1. MIT, Cambridge, USA

    James B. Orlin, Andreas S. Schulz & Rajan Udwani

Authors
  1. James B. Orlin
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  2. Andreas S. Schulz
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  3. Rajan Udwani
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Corresponding author

Correspondence to Rajan Udwani .

Editor information

Editors and Affiliations

  1. Université de Liège, Liège, Belgium

    Quentin Louveaux

  2. Technische Universität Berlin, Berlin, Germany

    Martin Skutella

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Orlin, J.B., Schulz, A.S., Udwani, R. (2016). Robust Monotone Submodular Function Maximization. In: Louveaux, Q., Skutella, M. (eds) Integer Programming and Combinatorial Optimization. IPCO 2016. Lecture Notes in Computer Science(), vol 9682. Springer, Cham. https://doi.org/10.1007/978-3-319-33461-5_26

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  • DOI: https://doi.org/10.1007/978-3-319-33461-5_26

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-33460-8

  • Online ISBN: 978-3-319-33461-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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