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 for antiferromagnetic spin systems in the tree non uniqueness region"):
  Abstract: A remarkable connection has been established for antiferromagnetic 2-spin systems, including the Ising and hard-core models, showing that the computational complexity of approximating the partition function for graphs with maximum degree D undergoes a phase transition that coincides with the statistical physics uniqueness/non-uniqueness phase transition on the infinite D-regular tree. Despite this clear picture for 2-spin systems, there is little known for multi-spin systems. We present the first analog of the above inapproximability results for multi-spin systems. #R##N#The main difficulty in previous inapproximability results was analyzing the behavior of the model on random D-regular bipartite graphs, which served as the gadget in the reduction. To this end one needs to understand the moments of the partition function. Our key contribution is connecting: (i) induced matrix norms, (ii) maxima of the expectation of the partition function, and (iii) attractive fixed points of the associated tree recursions (belief propagation). The view through matrix norms allows a simple and generic analysis of the second moment for any spin system on random D-regular bipartite graphs. This yields concentration results for any spin system in which one can analyze the maxima of the first moment. The connection to fixed points of the tree recursions enables an analysis of the maxima of the first moment for specific models of interest. #R##N#For k-colorings we prove that for even k, in the tree non-uniqueness region (which corresponds to k<D) it is NP-hard, unless NP=RP, to approximate the number of colorings for triangle-free D-regular graphs. Our proof extends to the antiferromagnetic Potts model, and, in fact, to every antiferromagnetic model under a mild condition.

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 "the complexity of ferromagnetic two spin systems with external fields":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "boolean approximate counting csps with weak conservativity and implications for ferromagnetic two spin")
  Member "approximation algorithms for two state anti ferromagnetic spin systems on bounded degree graphs":
    also connected through other hyperedges:
      - Hyperedge HE-3 (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-4 (induced by source paper "spectral independence in high dimensional expanders and applications to the hardcore model")
  Member "approximate counting via correlation decay in spin systems":
    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 "computational transition at the uniqueness threshold":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "spectral independence in high dimensional expanders and applications to the hardcore model")
  Member "a constructive proof of the general lovasz local lemma":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "scattering and sparse partitions and their applications")

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)