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 "approximating nash social welfare under submodular valuations through un matchings"):
  Abstract: We study the problem of approximating maximum Nash social welfare (NSW) when allocating m indivisible items among n asymmetric agents with submodular valuations. The NSW is a well-established notion of fairness and efficiency, defined as the weighted geometric mean of agents' valuations. For special cases of the problem with symmetric agents and additive(-like) valuation functions, approximation algorithms have been designed using approaches customized for these specific settings, and they fail to extend to more general settings. Hence, no approximation algorithm with factor independent of m is known either for asymmetric agents with additive valuations or for symmetric agents beyond additive(-like) valuations. #R##N#In this paper, we extend our understanding of the NSW problem to far more general settings. Our main contribution is two approximation algorithms for asymmetric agents with additive and submodular valuations respectively. Both algorithms are simple to understand and involve non-trivial modifications of a greedy repeated matchings approach. Allocations of high valued items are done separately by un-matching certain items and re-matching them, by processes that are different in both algorithms. We show that these approaches achieve approximation factors of O(n) and O(n log n) for additive and submodular case respectively, which is independent of the number of items. For additive valuations, our algorithm outputs an allocation that also achieves the fairness property of envy-free up to one item (EF1). #R##N#Furthermore, we show that the NSW problem under submodular valuations is strictly harder than all currently known settings with an e/(e-1) factor of the hardness of approximation, even for constantly many agents. For this case, we provide a different approximation algorithm that achieves a factor of e/(e-1), hence resolving it completely.

Includes members:
  Member "on fair division of indivisible items":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "efx exists for three agents")
  Member "a tale of santa claus hypergraphs and matroids":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "inapproximability results for scheduling with interval and resource restrictions")
  Member "approximating the nash social welfare with budget additive valuations":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "efx exists for three agents")
  Member "finding fair and efficient allocations":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "maximum nash welfare and other stories about efx")
  Member "convex program duality fisher markets and nash social welfare":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "maximum nash welfare and other stories about efx")
  Member "nash social welfare for indivisible items under separable piecewise linear concave utilities":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "efx exists for three agents")
  Member "nash social welfare matrix permanent and stable polynomials":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "efx exists for three agents")
  Member "apx hardness of maximizing nash social welfare with indivisible items":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "maximum nash welfare and other stories about efx")

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.GT(Computer Science and Game Theory)