human: Given a hyperedge-centered hypergraph: <hypergraph>, where the center hyperedge is induced by one source paper and its member nodes are the cited papers.

Details of the hypergraph:
Center hyperedge (induced by source paper "understanding popular matchings via stable matchings"):
  Abstract: An instance of the marriage problem is given by a graph G together with, for each vertex of G, a strict preference order over its neighbors. A matching M of Gis popular in the marriage instance if M does not lose a head-to-head election against anymatching where vertices are voters. Every stable matching is a min-size popular matching; another subclass of popular matchings that always exist and can be easily computed is theset of dominant matchings. A popular matching M is dominant if M wins the head-to-headelection against any larger matching. Thus every dominant matching is a max-size popularmatching and it is known that the set of dominant matchings is the linear image of the set ofstable matchings in an auxiliary graph. Results from the literature seem to suggest that stableand dominant matchings behave, from a complexity theory point of view, in a very similarmanner within the class of popular matchings.The goal of this paper is to show that indeed there are differences in the tractability of stableand dominant matchings, and to investigate further their importance for popular matchings.First, we show that it is easy to check if all popular matchings are also stable, however it isco-NP-hard to check if all popular matchings are also dominant. Second, we show how somenew and recent hardness results on popular matching problems can be deduced from the NP-hardnessof certain problems on stable matchings, also studied in this paper, thus showing thatstable matchings can be employed not only to show positive results on popular matching (as isknown), but also most negative ones. Problems for which we show new hardness results includefinding a min-size (resp. max-size) popular matching that is not stable (resp. dominant). Aknown result for which we give a new and simple proof is the NP-hardness of finding a popularmatching when G is non-bipartite.

Includes members:
  Member "max size popular matchings and extensions":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "popularity stability and the dominant matching polytope")
  Member "popular matching in roommates setting is np hard":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "quasi popular matchings optimality and extended formulations")
  Member "popular matchings and limits to tractability":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "computational complexity of stable marriage and stable roommates and their variants")
  Member "popular matchings with two sided preferences and one sided ties":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "popular branchings and their dual certificates")
  Member "popular edges and dominant matchings":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "quasi popular matchings optimality and extended formulations")

Question: Please tell me which class the source paper belongs to. The 40 classes are: cs.NA(Numerical Analysis), cs.MM(Multimedia), cs.LO(Logic in Computer Science), cs.CY(Computers and Society), cs.CR(Cryptography and Security), cs.DC(Distributed, Parallel, and Cluster Computing), cs.HC(Human-Computer Interaction), cs.CE(Computational Engineering, Finance, and Science), cs.NI(Networking and Internet Architecture), cs.CC(Computational Complexity), cs.AI(Artificial Intelligence), cs.MA(Multiagent Systems), cs.GL(General Literature), cs.NE(Neural and Evolutionary Computing), cs.SC(Symbolic Computation), cs.AR(Hardware Architecture), cs.CV(Computer Vision and Pattern Recognition), cs.GR(Graphics), cs.ET(Emerging Technologies), cs.SY(Systems and Control), cs.CG(Computational Geometry), cs.OH(Other Computer Science), cs.PL(Programming Languages), cs.SE(Software Engineering), cs.LG(Machine Learning), cs.SD(Sound), cs.SI(Social and Information Networks), cs.RO(Robotics), cs.IT(Information Theory), cs.PF(Performance), cs.CL(Computation and Language), cs.IR(Information Retrieval), cs.MS(Mathematical Software), cs.FL(Formal Languages and Automata Theory), cs.DS(Data Structures and Algorithms), cs.OS(Operating Systems), cs.GT(Computer Science and Game Theory), cs.DB(Databases), cs.DL(Digital Libraries), cs.DM(Discrete Mathematics). Directly output the class name.

gpt: cs.DM(Discrete Mathematics)