The Minimum Entropy Submodular Set Cover Problem

Conference paper

DOI: 10.1007/978-3-319-30000-9_23

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9618)
Cite this paper as:
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

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.

Keywords

Submodular set cover Minimum entropy Approximation algorithms 

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Gabriel Istrate
    • 1
    • 2
  • Cosmin Bonchiş
    • 1
    • 2
  • Liviu P. Dinu
    • 3
  1. 1.Department of Computer ScienceWest University of TimişoaraTimişoaraRomania
  2. 2.e-Austria Research InstituteTimişoaraRomania
  3. 3.Faculty of Mathematics and Computer ScienceUniversity of BucharestBucharestRomania

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