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The Minimum Entropy Submodular Set Cover Problem

Autori: Gabriel Istrate, Cosmin Bonchis, Liviu P. Dinu

Editorial: Proceedings of the 10th International Conference on Language and Automata Theory and Applications (LATA' 2016), Lecture Notes in Computer Science vol. 9618, p.295-306, Springer Verlag, 2016.


We study minimum entropy submodular set cover, a variant of the submodular set cover problem (Wolsey, Fujito, etc) that generalizes the minimum entropy set cover problem (Halperin and Karp, Cardinal et al.)

We give a general bound of 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.