On Simplified Group Activity Selection

Darmann, Andreas; Döcker, Janosch; Dorn, Britta; Lang, Jérôme; Schneckenburger, Sebastian

doi:10.1007/978-3-319-67504-6_18

Cited by 9 publications

(9 citation statements)

References 10 publications

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“…For our reduction we start from a restricted version of the so called GROUP ACTIVITY SELECTION problem (Darmann et al 2017), called the SIMPLE GROUP AC-TIVITY SELECTION PROBLEM (SGASP). To distinguish terminology between the GROUP ACTIVITY SELECTION problem and our HDG setting, we use slightly different terminology for that problem.…”

Section: Parameterizing By the Smaller Of Two Color Classesmentioning

confidence: 99%

“…Apart from requiring non-trivial insight into the structure of a possible solution, the approaches used to solve the Boehmer and Elkind (2020a): when the number of colors (γ) is 2, is Nash-stable HDG fixed-parameter tractable when parameterized by the size of the smaller color class? Here, we provide a highly non-elementary reduction from a variant of the GROUP ACTIVITY SELECTION problem (Darmann et al 2017;Eiben, Ganian, and Ordyniak 2018) which excludes fixed-parameter tractability.…”

Section: Introductionmentioning

confidence: 99%

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Hedonic Diversity Games: A Complexity Picture with More than Two Colors

Ganian¹,

Hamm²,

Knop³

et al. 2022

Preprint

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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 some initial complexitytheoretic and existential results concerning Nash and individually stable outcomes. Here, we design new algorithms accompanied with lower bounds which provide a complete 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). ℓ i=1 C i = N and all C i 's are pairwise disjoint. We call

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Section: Parameterizing By the Smaller Of Two Color Classesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Hedonic Diversity Games: A Complexity Picture with More than Two Colors

Ganian¹,

Hamm²,

Knop³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Apart from requiring non-trivial insight into the structure of a possible solution, the approaches used to solve the tractable fragments vary greatly from one another: the fixedparameter algorithm w.r. Boehmer and Elkind (2020a): when the number of colors (γ) is 2, is Nash-stable HDG fixed-parameter tractable when parameterized by the size of the smaller color class? Here, we provide a highly non-elementary reduction from a variant of the GROUP ACTIVITY SELECTION problem (Darmann et al 2017;Eiben, Ganian, and Ordyniak 2018) which excludes fixed-parameter tractability.…”

Section: Introductionmentioning

confidence: 99%

Hedonic Diversity Games: A Complexity Picture with More than Two Colors

Ganian

Hamm

Knop

et al. 2022

AAAI

View full text Add to dashboard Cite

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).

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“…Several stability conditions have been defined and used for this problem, including Nash stability. GASP was introduced by Darmann et al (2012; and has been studied in various settings [Lee and Williams, 2017b;Darmann et al, 2017a;Igarashi et al, 2017a;2017c;Gupta et al, 2017].…”

Section: Introductionmentioning

confidence: 99%

A Structural Approach to Activity Selection

Eiben

Ganian

Ordyniak

2018

Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence

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The general task of finding an assignment of agents to activities under certain stability and rationality constraints has led to the introduction of two prominent problems in the area of computational social choice: Group Activity Selection (GASP) and Stable Invitations (SIP). Here we introduce and study the Comprehensive Activity Selection Problem, which naturally generalizes both of these problems. In particular, we apply the parameterized complexity paradigm, which has already been successfully employed for SIP and GASP. While previous work has focused strongly on parameters such as solution size or number of activities, here we focus on parameters which capture the complexity of agent-to-agent interactions. Our results include a comprehensive complexity map for CAS under various restrictions on the number of activities in combination with restrictions on the complexity of agent interactions.

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On Simplified Group Activity Selection

Cited by 9 publications

References 10 publications

Hedonic Diversity Games: A Complexity Picture with More than Two Colors

Hedonic Diversity Games: A Complexity Picture with More than Two Colors

Hedonic Diversity Games: A Complexity Picture with More than Two Colors

A Structural Approach to Activity Selection

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