Minimum Entropy Submodular Optimization (and Fairness in Cooperative Games)
Abstract
We study minimum entropy submodular optimization, a common generalization of the minimum entropy set cover problem, studied earlier by Cardinal et al., and the submodular set cover problem. 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) the definition of worst-case approaches to fairness in concave cooperative games, similar to the notion of price of anarchy in noncooperative settings.
Cite
@article{arxiv.1402.4343,
title = {Minimum Entropy Submodular Optimization (and Fairness in Cooperative Games)},
author = {Cosmin Bonchiş and Gabriel Istrate},
journal= {arXiv preprint arXiv:1402.4343},
year = {2014}
}