5 research outputs found
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).Comment: 9 pages, long version of accepted AAMAS-17 pape
Hedonic Games with Graph-restricted Communication
We study hedonic coalition formation games in which cooperation among the
players is restricted by a graph structure: a subset of players can form a
coalition if and only if they are connected in the given graph. We investigate
the complexity of finding stable outcomes in such games, for several notions of
stability. In particular, we provide an efficient algorithm that finds an
individually stable partition for an arbitrary hedonic game on an acyclic
graph. We also introduce a new stability concept -in-neighbor stability- which
is tailored for our setting. We show that the problem of finding an in-neighbor
stable outcome admits a polynomial-time algorithm if the underlying graph is a
path, but is NP-hard for arbitrary trees even for additively separable hedonic
games; for symmetric additively separable games we obtain a PLS-hardness
result