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Computer Science > Computational Complexity

arXiv:1908.11554 (cs)
[Submitted on 30 Aug 2019 (v1), last revised 22 Oct 2019 (this version, v2)]

Title:Computational Complexity of Hedonic Games on Sparse Graphs

Authors: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.
Subjects: Computational Complexity (cs.CC)
Cite as: arXiv:1908.11554 [cs.CC]
  (or arXiv:1908.11554v2 [cs.CC] for this version)
  https://doi.org/10.48550/arXiv.1908.11554

Submission history

From: Yasuhide Maei [view email]
[v1] Fri, 30 Aug 2019 06:26:11 UTC (1,359 KB)
[v2] Tue, 22 Oct 2019 12:22:00 UTC (1,690 KB)
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