Ganian, R., Hamm, T., Knop, D., Schierreich, Š., & Suchý, O. (2022). Hedonic Diversity Games: A Complexity Picture with More than Two Colors. In Proceedings of the 36th AAAI Conference on Artificial Intelligence (pp. 5034–5042). AAAI Press. https://doi.org/10.1609/aaai.v36i5.20435
Hedonic diversity games are a variant of the classical Hedonic games designed to better model a variety of questions concerning diversity and fairness. Previous works mainly targeted the case with two diversity classes (represented as colors in the model) and provided a set of initial complexity-theoretic and existential results concerning Nash and Individually stable outcomes. Here, we design new algorithms accompanied with lower bounds which provide a full parameterized-complexity picture for computing Nash and Individually stable outcomes with respect to the most natural parameterizations of the problem. Crucially, our results hold for general Hedonic diversity games where the number of colors is not necessarily restricted to two, and show that---apart from two trivial cases---a necessary condition for tractability in this setting is that the number of colors is bounded by the parameter. Moreover, for the special case of two colors we resolve an open question asked in previous work~(Boehmer and Elkind, AAAI 2020).
en
Project title:
New Frontiers for Parameterized Complexity: P31336-N35 (Fonds zur Förderung der wissenschaftlichen Forschung (FWF)) Parameterisierte Analyse in der Künstlichen Intelligenz: Y1329-N (Fonds zur Förderung der wissenschaftlichen Forschung (FWF)) Structural Approaches in Stability Under Diversity Constraints: CZ 05/2021 (OeAD Österr.Austauschdienst GmbH Geschäftsstelle Wien)
-
Project (external):
OeAD bilateral Czech-Austrian WTZ-funding Programme Austrian Science Fund (FWF) OP VVV MEYS Grant Agency of the Czech Technical University in Prague