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 "convex program duality fisher markets and nash social welfare"):
  Abstract: We study Fisher markets and the problem of maximizing the Nash social welfare (NSW), and show several closely related new results. In particular, we obtain: #R##N#-- A new integer program for the NSW maximization problem whose fractional relaxation has a bounded integrality gap. In contrast, the natural integer program has an unbounded integrality gap. #R##N#-- An improved, and tight, factor 2 analysis of the algorithm of [7]; in turn showing that the integrality gap of the above relaxation is at most 2. The approximation factor shown by [7] was $2e^{1/e} \approx 2.89$. #R##N#-- A lower bound of $e^{1/e}\approx 1.44$ on the integrality gap of this relaxation. #R##N#-- New convex programs for natural generalizations of linear Fisher markets and proofs that these markets admit rational equilibria. #R##N#These results were obtained by establishing connections between previously known disparate results, and they help uncover their mathematical underpinnings. We show a formal connection between the convex programs of Eisenberg and Gale and that of Shmyrev, namely that their duals are equivalent up to a change of variables. Both programs capture equilibria of linear Fisher markets. By adding suitable constraints to Shmyrev's program, we obtain a convex program that captures equilibria of the spending-restricted market model defined by [7] in the context of the NSW maximization problem. Further, adding certain integral constraints to this program we get the integer program for the NSW mentioned above. #R##N#The basic tool we use is convex programming duality. In the special case of convex programs with linear constraints (but convex objectives), we show a particularly simple way of obtaining dual programs, putting it almost at par with linear program duality. This simple way of finding duals has been used subsequently for many other applications.

Includes members:
  Member "when does the price of anarchy tend to 1 in large walrasian auctions and fisher markets":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "walrasian dynamics in multi unit markets")
  Member "apx hardness of maximizing nash social welfare with indivisible items":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "maximum nash welfare and other stories about efx")
  Member "welfare maximization with production costs a primal dual approach":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "reducing inefficiency in carbon auctions with imperfect competition")
  Member "online packing and covering framework with convex objectives":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "online covering with sum of ell_q norm objectives")
  Member "selfishmigrate a scalable algorithm for non clairvoyantly scheduling heterogeneous processors":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "a unifying optimal control framework for online job scheduling with general cost functions")
  Member "a rational convex program for linear arrow debreu markets":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "proportional dynamics in exchange economies")
  Member "market equilibrium with transaction costs":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "robust market equilibria with uncertain preferences")

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)