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 "approximation via correlation decay when strong spatial mixing fails"):
  Abstract: Approximate counting via correlation decay is the core algorithmic technique used in the sharp delineation of the computational phase transition that arises in the approximation of the partition function of anti-ferromagnetic two-spin models. #R##N#Previous analyses of correlation-decay algorithms implicitly depended on the occurrence of strong spatial mixing (SSM). This means that one uses worst-case analysis of the recursive procedure that creates the sub-instances. We develop a new analysis method that is more refined than the worst-case analysis. We take the shape of instances in the computation tree into consideration and amortise against certain "bad" instances that are created as the recursion proceeds. This enables us to show correlation decay and to obtain an FPTAS even when SSM fails. #R##N#We apply our technique to the problem of approximately counting independent sets in hypergraphs with degree upper-bound Delta and with a lower bound k on the arity of hyperedges. Liu and Lin gave an FPTAS for k>=2 and Delta =3 and Delta =8. #R##N#Our technique also applies for larger values of k, giving an FPTAS for k>=Delta. This bound is not substantially stronger than existing randomised results in the literature. Nevertheless, it gives the first deterministic approximation scheme in this regime. Moreover, unlike existing results, it leads to an FPTAS for counting dominating sets in regular graphs with sufficiently large degree. #R##N#We further demonstrate that approximately counting independent sets in hypergraphs is NP-hard even within the uniqueness regime.

Includes members:
  Member "inapproximability of the partition function for the antiferromagnetic ising and hard core models":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "lower bounds for testing graphical models colorings and antiferromagnetic ising models")
  Member "fptas for hardcore and ising models on hypergraphs":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "the ising partition function zeros and deterministic approximation")
  Member "the complexity of approximately counting in 2 spin systems on k uniform bounded degree hypergraphs":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "the ising partition function zeros and deterministic approximation")
  Member "spatial mixing and approximate counting for potts model on graphs with bounded average degree":
    also connected through other hyperedges:
      (none)
  Member "approximately counting locally optimal structures":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "counting independent sets in cocomparability graphs")
  Member "spatial mixing and the connective constant optimal bounds":
    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 "fptas for counting monotone cnf":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "computing the independence polynomial in shearer s region for the lll")
  Member "approximation algorithms for two state anti ferromagnetic spin systems on bounded degree graphs":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "efficient distance approximation for structured high dimensional distributions via learning")

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)