Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computational Complexity of Hedonic Games on Sparse Graphs   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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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
2
The categories of this paper are: math
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The categories of this paper are: eess
3
The categories of this paper are: physics
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The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph