A Structural Approach to Activity Selection

Eiben, Eduard; Ganian, Robert; Ordyniak, Sebastian

doi:10.24963/ijcai.2018/28

Cited by 10 publications

(11 citation statements)

References 12 publications

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“…SGASP is fixed-parameter tractable when parameterized by t + a. This is the only fixed-parameter tractability result presented in the paper, and is essentially tight: it was recently shown that SGASP is W [1]-hard when parameterized by a alone [9], and the W [1]-hardness of the problem when parameterized by t is obtained in this paper. Our first step towards obtaining the desired fixed-parameter algorithm for SGASP is to show that every YES-instance has a solution which is acyclic-in particular, a solution with no cycles formed by interactions between activities and agent types (captured in terms of the incidence graph G of an assignment).…”

Section: Introductionmentioning

confidence: 53%

“…It is therefore natural to study these problems through the lens of parameterized complexity [8,2]. Apart from parameterizing by the solution size (i.e., the number of agents assigned to any activity in a solution) [19], the perhaps most prominent parameterizations thus far have been the number of activities, the number of agents, and in the case of gGASP structural parameterizations tied to the structure of the network such as treewidth [6,18,15,9]. Consequently, the parameterized complexity of all three variants of GASP w.r.t.…”

Section: Introductionmentioning

confidence: 99%

“…One prominent result in this direction has been recently obtained by Gupta et al ([15]), showing that gGASP is fixed-parameter tractable parameterized by the number of activities if the network has constant treewidth. For SGASP, it was recently shown that the problem is also W [1]-hard when parameterized by the number of activities [9], and hence the only small gap left was the complexity of this problem parameterized by the number of agents. For completeness, we resolve this question in our concluding remarks by giving a fixed-parameter algorithm.…”

Section: Introductionmentioning

confidence: 99%

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Group Activity Selection with Few Agent Types

Ganian

Ordyniak

Rahul

2018

Preprint

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The Group Activity Selection Problem (GASP) models situations where a group of agents needs to be distributed to a set of activities while taking into account preferences of the agents w.r.t. individual activities and activity sizes. The problem, along with its two previously proposed variants sGASP and gGASP, has been studied in the parameterized complexity setting with various parameterizations, such as number of agents, number of activities and solution size. However, the complexity of the problem parameterized by the number of types of agents, a parameter motivated and proposed already in the paper that introduced GASP, has so far remained open.In this paper we establish the complexity map for GASP, sGASP and gGASP when the number of types of agents is the parameter. Our positive results, consisting of one fixed-parameter algorithm and one XP algorithm, rely on a combination of novel Subset Sum machinery (which may be of general interest) and identifying certain compression steps which allow us to focus on solutions which are "acyclic". These algorithms are complemented by matching lower bounds, which among others answer an open question of Gupta, Roy, Saurabh and Zehavi (2017). In this direction, the techniques used to establish W[1]-hardness of sGASP are of particular interest: as an intermediate step, we use Sidon sequences to show the W[1]-hardness of a highly restricted variant of multi-dimensional Subset Sum, which may find applications in other settings as well.

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Section: Introductionmentioning

confidence: 53%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Group Activity Selection with Few Agent Types

Ganian

Ordyniak

Rahul

2018

Preprint

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“…Our work is also related to models from cooperative game theory, such as hedonic games [11,22,5] and group activity selection games [19,18,21]. In hedonic games, the agents form coalitions and their utilities are decided solely by the members in the coalition, without any resource in the model.…”

Section: Related Workmentioning

confidence: 99%

Fair Resource Sharing with Externailities

Gan,

Li,

2020

Preprint

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We study a fair resource sharing problem, where a set of resources are to be shared among a set of agents. Each agent demands one resource and each resource can serve a limited number of agents. An agent cares about what resource they get as well as the externalities imposed by their mates, whom they share the same resource with. Apparently, the strong notion of envyfreeness, where no agent envies another for their resource or mates, cannot always be achieved and we show that even to decide the existence of such a strongly envy-free assignment is an intractable problem. Thus, a more interesting question is whether (and in what situations) a relaxed notion of envy-freeness, the Pareto envy-freeness, can be achieved: an agent i envies another agent j only when i envies both the resource and the mates of j. In particular, we are interested in a dorm assignment problem, where students are to be assigned to dorms with the same capacity and they have dichotomous preference over their dorm-mates. We show that when the capacity of the dorms is 2, a Pareto envy-free assignment always exists and we present a polynomial-time algorithm to compute such an assignment; nevertheless, the result fails to hold immediately when the capacities increase to 3, in which case even Pareto envy-freeness cannot be guaranteed. In addition to the existential results, we also investigate the implications of envy-freeness on proportionality in our model and show that envy-freeness in general implies approximations of proportionality.

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“…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%

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

Ganian¹,

Hamm²,

Knop³

et al. 2022

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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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A Structural Approach to Activity Selection

Cited by 10 publications

References 12 publications

Group Activity Selection with Few Agent Types

Group Activity Selection with Few Agent Types

Fair Resource Sharing with Externailities

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

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