Computational Complexity of Hedonic Games on Sparse Graphs

Tesshu Hanaka; Hironori Kiya; Yasuhide Maei; Hirotaka Ono

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arXiv · 1908.11554

Computational Complexity of Hedonic Games on Sparse Graphs

Tesshu Hanaka·Hironori Kiya·Yasuhide Maei·Hirotaka Ono

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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.

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Tesshu Hanaka, Hironori Kiya, Yasuhide Maei, Hirotaka Ono. 2019-08-30. Computational Complexity of Hedonic Games on Sparse Graphs. https://arxiv.org/abs/1908.11554

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