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 "smoothed efficient algorithms and reductions for network coordination games"):
  Abstract: Worst-case hardness results for most equilibrium computation problems have raised the need for beyond-worst-case analysis. To this end, we study the smoothed complexity of finding pure Nash equilibria in Network Coordination Games, a PLS-complete problem in the worst case. This is a potential game where the sequential-better-response algorithm is known to converge to a pure NE, albeit in exponential time. First, we prove polynomial (resp. quasi-polynomial) smoothed complexity when the underlying game graph is a complete (resp. arbitrary) graph, and every player has constantly many strategies. We note that the complete graph case is reminiscent of perturbing all parameters, a common assumption in most known smoothed analysis results. #R##N#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 recent result of [BCC18] gives an alternate $O(n^8)$-time smoothed algorithm for the $2$-strategy case. This notion of reduction allows for the extension of smoothed efficient algorithms from one problem to another. #R##N#For the first set of results, we develop techniques to bound the probability that an (adversarial) better-response sequence makes slow improvements on the potential. Our approach combines and generalizes the local-max-cut approaches of [ER14,ABPW17] to handle the multi-strategy case: it requires a careful definition of the matrix which captures the increase in potential, a tighter union bound on adversarial sequences, and balancing it with good enough rank bounds. We believe that the approach and notions developed herein could be of interest in addressing the smoothed complexity of other potential and/or congestion games.

Includes members:
  Member "improving the smoothed complexity of flip for max cut problems":
    also connected through other hyperedges:
      (none)
  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 "efficient local search in coordination games on graphs":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "coordination games on weighted directed graphs")
  Member "settling the complexity of computing approximate two player nash equilibria":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "complexity theory game theory and economics the barbados lectures")
  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 "the price of anarchy in auctions":
    also connected through other hyperedges:
      - Hyperedge HE-5 (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-6 (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-7 (induced by source paper "consenus halving does it ever get easier")

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)