Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Parameterized Complexity of Group Activity Selection Problems on
  Social Networks   In Group Activity Selection Problem (GASP), players form coalitions to
participate in activities and have preferences over pairs of the form
(activity, group size). Recently, Igarashi et al. have initiated the study of
group activity selection problems on social networks (gGASP): a group of
players can engage in the same activity if the members of the group form a
connected subset of the underlying communication structure. Igarashi et al.
have primarily focused on Nash stable outcomes, and showed that many associated
algorithmic questions are computationally hard even for very simple networks.
In this paper we study the parameterized complexity of gGASP with respect to
the number of activities as well as with respect to the number of players, for
several solution concepts such as Nash stability, individual stability and core
stability. The first parameter we consider in the number of activities. For
this parameter, we propose an FPT algorithm for Nash stability for the case
where the social network is acyclic and obtain a W[1]-hardness result for
cliques (i.e., for classic GASP); similar results hold for individual
stability. In contrast, finding a core stable outcome is hard even if the
number of activities is bounded by a small constant, both for classic GASP and
when the social network is a star. Another parameter we study is the number of
players. While all solution concepts we consider become polynomial-time
computable when this parameter is bounded by a constant, we prove W[1]-hardness
results for cliques (i.e., for classic GASP).

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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: math
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The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc