Computational Complexity of Hedonic Games on Sparse Graphs
Computational Complexity
2019-10-23 v2
Abstract
The additively separable hedonic game (ASHG) is a model of coalition formation games on graphs. In this paper, we intensively and extensively investigate the computational complexity of finding several desirable solutions, such as a Nash stable solution, a maximum utilitarian solution, and a maximum egalitarian solution in ASHGs on sparse graphs including bounded-degree graphs, bounded-treewidth graphs, and near-planar graphs. For example, we show that finding a maximum egalitarian solution is weakly NP-hard even on graphs of treewidth 2, whereas it can be solvable in polynomial time on trees. Moreover, we give a pseudo fixed parameter algorithm when parameterized by treewidth.
Keywords
Cite
@article{arxiv.1908.11554,
title = {Computational Complexity of Hedonic Games on Sparse Graphs},
author = {Tesshu Hanaka and Hironori Kiya and Yasuhide Maei and Hirotaka Ono},
journal= {arXiv preprint arXiv:1908.11554},
year = {2019}
}