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 "inapproximability after uniqueness phase transition in two spin systems"):
  Abstract: A two-state spin system is specified by a 2 x 2 matrix #R##N#A = {A_{0,0} A_{0,1}, A_{1,0} A_{1,1}} = {\beta 1, 1 \gamma} where \beta, \gamma \ge 0. Given an input graph G=(V,E), the partition function Z_A(G) of a system is defined as #R##N#Z_A(G) = \sum_{\sigma: V -> {0,1}} \prod_{(u,v) \in E} A_{\sigma(u), \sigma(v)} #R##N#We prove inapproximability results for the partition function in the region specified by the non-uniqueness condition from phase transition for the Gibbs measure. More specifically, assuming NP \ne RP, for any fixed \beta, \gamma in the unit square, there is no randomized polynomial-time algorithm that approximates Z_A(G) for d-regular graphs G with relative error \epsilon = 10^{-4}, if d = \Omega(\Delta(\beta,\gamma)), where \Delta(\beta,\gamma) > 1/(1-\beta\gamma) is the uniqueness threshold. Up to a constant factor, this hardness result confirms the conjecture that the uniqueness phase transition coincides with the transition from computational tractability to intractability for Z_A(G). We also show a matching inapproximability result for a region of parameters \beta, \gamma outside the unit square, and all our results generalize to partition functions with an external field.

Includes members:
  Member "approximation algorithms for two state anti ferromagnetic spin systems on bounded degree graphs":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "efficient distance approximation for structured high dimensional distributions via learning")
  Member "correlation decay up to uniqueness in spin systems":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "spectral independence in high dimensional expanders and applications to the hardcore model")
  Member "complexity of counting csp with complex weights":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "optimal polynomial time compression for boolean max csp")
  Member "approximate counting via correlation decay in spin systems":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "spectral independence in high dimensional expanders and applications to the hardcore model")
  Member "improved inapproximability results for counting independent sets in the hard core model":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "spectral independence in high dimensional expanders and applications to the hardcore model")
  Member "non negative weighted csps an effective complexity dichotomy":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "the complexity of approximating conservative counting csps")
  Member "computational transition at the uniqueness threshold":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "spectral independence in high dimensional expanders and applications to the hardcore model")
  Member "a decidable dichotomy theorem on directed graph homomorphisms with non negative weights":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "a dichotomy for bounded degree graph homomorphisms with nonnegative weights")

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)