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 "nash equilibrium in smoothed polynomial time for network coordination games"):
  Abstract: Extensive work in the last two decades has led to deep insights into the worst case complexity of computing Nash equilibria (NE). However, largely negative results have raised the need for beyond worst-case analysis of these problems. In this paper, we study the smoothed complexity of finding pure NE in Network Coordination Games, a PLS-complete problem in the worst case. First, we prove (quasi-) polynomial smoothed complexity when the underlying game graph is an (arbitrary) complete graph, and every player has constantly many strategies. To the best of our knowledge, ours is the first smoothed efficient algorithm for a Nash equilibrium problem that is hard in the worst case. We note that the complete graph case is reminiscent of perturbing all parameters, a common assumption in almost all known smoothed efficient analysis. Second, we define a notion of smoothness-preserving reduction among search problems, and obtain reductions from 2-strategy network coordination games to local-max-cut, and from k-strategy games (with arbitrary k) to local-max-cut up to two flips. The former, together with the known smoothed efficient algorithm for the local-max-cut problem, gives an alternate efficient smoothed algorithm for the 2-strategy games. This notion of reduction may be utilized to extend smoothed efficient algorithms from one problem to another. For the first set of results, we develop techniques to analyze the probability of a slow increase in potential during the better-response algorithm for a perturbed game, by building on and significantly extending the recent approaches for smoothed analysis of local-max-cut [ER'14,ABPW'17]. We note that network coordination games are far more general than local-max-cut since the latter reduces to a 2-strategy case of the former. Our techniques may be of independent interest to perform smoothed analysis of other potential/congestion games.

Includes members:
  Member "near optimal communication lower bounds for approximate nash equilibria":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "complexity theory game theory and economics the barbados lectures")
  Member "local max cut in smoothed polynomial time":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "node max cut and computing equilibria in linear weighted congestion games")
  Member "an empirical study on computing equilibria in polymatrix games":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "tree polymatrix games are ppad hard")
  Member "communication complexity of approximate nash equilibria":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "complexity theory game theory and economics the barbados lectures")
  Member "inapproximability of nash equilibrium":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "the complexity of interactively learning a stable matching by trial and error")
  Member "constant rank bimatrix games are ppad hard":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "consenus halving does it ever get easier")
  Member "query complexity of approximate nash equilibria":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "complexity theory game theory and economics the barbados lectures")
  Member "bilinear games polynomial time algorithms for rank based subclasses":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "computing stackelberg equilibria of large general sum games")

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.CC(Computational Complexity)