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The Minimum Entropy Submodular Set Cover Problem

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Language and Automata Theory and Applications (LATA 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9618))

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Abstract

We study Minimum Entropy Submodular Set Cover, a variant of the Submodular Set Cover problem (Wolsey [21], Fujito [8], etc.) that generalizes the Minimum Entropy Set Cover problem (Halperin and Karp [11], Cardinal et al. [4]) We give a general bound on the approximation performance of the greedy algorithm using an approach that can be interpreted in terms of a particular type of biased network flows. As an application we rederive known results for the Minimum Entropy Set Cover and Minimum Entropy Orientation problems, and obtain a nontrivial bound for a new problem called the Minimum Entropy Spanning Tree problem. The problem can be applied to (and is partly motivated by) a worst-case approach to fairness in concave cooperative games.

G. Istrate and C. Bonchiş were supported by IDEI Grant PN-II-ID-PCE-2011-3-0981. L.P. Dinu was supported by UEFISCDI, PNII-ID-PCE-2011-3-0959.

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Notes

  1. 1.

    The problem is NP-hard, rather than NP-complete, since its specification involves general real numbers that may put it outside class NP.

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Author information

Authors and Affiliations

  1. Department of Computer Science, West University of Timişoara, Bd. V. Pârvan 4, Timişoara, Romania

    Gabriel Istrate & Cosmin Bonchiş

  2. e-Austria Research Institute, Bd. V. Pârvan 4, cam. 045 B, Timişoara, Romania

    Gabriel Istrate & Cosmin Bonchiş

  3. Faculty of Mathematics and Computer Science, University of Bucharest, Bucharest, Romania

    Liviu P. Dinu

Authors
  1. Gabriel Istrate
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  2. Cosmin Bonchiş
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  3. Liviu P. Dinu
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Corresponding author

Correspondence to Gabriel Istrate .

Editor information

Editors and Affiliations

  1. Rovira i Virgili University, Tarragona, Spain

    Adrian-Horia Dediu

  2. Czech Technical University, Prague, Czech Republic

    Jan Janoušek

  3. Rovira i Virgili University, Tarragona, Spain

    Carlos Martín-Vide

  4. Justus Liebig University Giessen, Gießen, Germany

    Bianca Truthe

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Istrate, G., Bonchiş, C., Dinu, L.P. (2016). The Minimum Entropy Submodular Set Cover Problem. In: Dediu, AH., Janoušek, J., Martín-Vide, C., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2016. Lecture Notes in Computer Science(), vol 9618. Springer, Cham. https://doi.org/10.1007/978-3-319-30000-9_23

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  • DOI: https://doi.org/10.1007/978-3-319-30000-9_23

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  • Print ISBN: 978-3-319-29999-0

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