English

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}
}
R2 v1 2026-06-23T11:00:39.077Z