Working Together: Committee Selection and the Supermodular Degree

Izsak, Rani

doi:10.1007/978-3-319-71682-4_7

Cited by 6 publications

(3 citation statements)

References 16 publications

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“…Through set functions, Izsak allows voters to express their preferences of being represented by several specific candidates together; e.g., the score a voter gives to two candidates together can be higher than the sum of their individual scores (say, if they are known to work extremely well together). As set functions might be too complex, Izsak considers preference elicitation and algorithms based on the supermodular degree (Feige and Izsak 2013) and showed that existing algorithms (Feldman and Izsak 2014;2017) can be used to obtain approximation guarantees that depend on the supermodular degree. The supermodular degree, however, might be too large when some candidates have synergy with many other candidates.…”

Section: Related Workmentioning

confidence: 99%

Committee Selection with Intraclass and Interclass Synergies

Izsak

Talmon

Woeginger

2018

AAAI

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Voting is almost never done in void, as usually there are some relations between the alternatives on which the voters vote on. These relations shall be taken into consideration when selecting a winning committee of some given multiwinner election. As taking into account all possible relations between the alternatives is generally computationally intractable, in this paper we consider classes of alternatives; intuitively, the number of classes is significantly smaller than the number of alternatives, and thus there is some hope in reaching computational tractability. We model both intraclass relations and interclass relations by functions, which we refer to as synergy functions, and study the computational complexity of identifying the best committee, taking into account those synergy functions. Our model accommodates both positive and negative relations between alternatives; further, our efficient algorithms can also deal with a rich class of diversity wishes, which we show how to model using synergy functions.

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Section: Related Workmentioning

confidence: 99%

Committee Selection with Intraclass and Interclass Synergies

Izsak

Talmon

Woeginger

2018

AAAI

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“…Feldman and Izsak (2014) generalized these results to function maximization subject to kextendible system constraints (a generalization of the intersection of k matroids). These concepts have also been applied in an online setting (Feldman and Izsak 2017), and in the context of efficiency of auctions (Feldman et al 2016), optimization of SDN upgrades (Poularakis et al 2017) and committee selection (Izsak 2017). Some related complexity measures are the submodularity ratio (Das and Kempe 2011) and MPH (Feige et al 2015).…”

Section: Introductionmentioning

confidence: 99%

Cooperative Games With Bounded Dependency Degree

Igarashi

Izsak

Elkind

2018

AAAI

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Cooperative games provide a framework to study cooperation among self-interested agents. They offer a number of solution concepts describing how the outcome of the cooperation should be shared among the players. Unfortunately, computational problems associated with many of these solution concepts tend to be intractable---NP-hard or worse. In this paper, we incorporate complexity measures recently proposed by Feige and Izsak (2013), called dependency degree and supermodular degree, into the complexity analysis of coopera- tive games. We show that many computational problems for cooperative games become tractable for games whose dependency degree or supermodular degree are bounded. In particular, we prove that simple games admit efficient algorithms for various solution concepts when the supermodular degree is small; further, we show that computing the Shapley value is always in FPT with respect to the dependency degree. Finally, we observe that, while determining the dependency among players is computationally hard, there are efficient algorithms for special classes of games.

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Section: Introductionmentioning

confidence: 99%

Cooperative Games with Bounded Dependency Degree

Igarashi¹,

Izsak²,

Elkind³

2017

Preprint

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Cooperative games provide a framework to study cooperation among self-interested agents. They offer a number of solution concepts describing how the outcome of the cooperation should be shared among the players. Unfortunately, computational problems associated with many of these solution concepts tend to be intractable-NP-hard or worse. In this paper, we incorporate complexity measures recently proposed by Feige and Izsak (2013), called dependency degree and supermodular degree, into the complexity analysis of cooperative games. We show that many computational problems for cooperative games become tractable for games whose dependency degree or supermodular degree are bounded. In particular, we prove that simple games admit efficient algorithms for various solution concepts when the supermodular degree is small; further, we show that computing the Shapley value is always in FPT with respect to the dependency degree. Finally, we note that, while determining the dependency among players is computationally hard, there are efficient algorithms for special classes of games.

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Working Together: Committee Selection and the Supermodular Degree

Cited by 6 publications

References 16 publications

Committee Selection with Intraclass and Interclass Synergies

Committee Selection with Intraclass and Interclass Synergies

Cooperative Games With Bounded Dependency Degree

Cooperative Games with Bounded Dependency Degree

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