human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "ferromagnetic potts model refined bis hardness and related results"
  Abstract: Recent results establish for 2-spin antiferromagnetic systems that the computational complexity of approximating the partition function on graphs of maximum degree D undergoes a phase transition that coincides with the uniqueness phase transition on the infinite D-regular tree. For the ferromagnetic Potts model we investigate whether analogous hardness results hold. Goldberg and Jerrum showed that approximating the partition function of the ferromagnetic Potts model is at least as hard as approximating the number of independent sets in bipartite graphs (#BIS-hardness). We improve this hardness result by establishing it for bipartite graphs of maximum degree D. We first present a detailed picture for the phase diagram for the infinite D-regular tree, giving a refined picture of its first-order phase transition and establishing the critical temperature for the coexistence of the disordered and ordered phases. We then prove for all temperatures below this critical temperature that it is #BIS-hard to approximate the partition function on bipartite graphs of maximum degree D. As a corollary, it is #BIS-hard to approximate the number of k-colorings on bipartite graphs of maximum degree D when k <= D/(2 ln D). #R##N#The #BIS-hardness result for the ferromagnetic Potts model uses random bipartite regular graphs as a gadget in the reduction. The analysis of these random graphs relies on recent connections between the maxima of the expectation of their partition function, attractive fixpoints of the associated tree recursions, and induced matrix norms. We extend these connections to random regular graphs for all ferromagnetic models and establish the Bethe prediction for every ferromagnetic spin system on random regular graphs. We also prove for the ferromagnetic Potts model that the Swendsen-Wang algorithm is torpidly mixing on random D-regular graphs at the critical temperature for large q.

Connected through hyperedge HE-1 (induced by source paper "efficient algorithms for the potts model on small set expanders"):
  with members:
    - "counting independent sets in unbalanced bipartite graphs"
    - "fast algorithms at low temperatures via markov chains"
    - "statistical physics approaches to unique games"
    - "algorithms for bis hard problems on expander graphs"
    - "algorithmic pirogov sinai theory"
    - "partitioning into expanders"
    - "improved cheeger s inequality analysis of spectral partitioning algorithms through higher order spectral gap"
    - "approximating the expansion profile and almost optimal local graph clustering"

Connected through hyperedge HE-2 (induced by source paper "counting independent sets and colorings on random regular bipartite graphs"):
  with members:
    - "algorithms for bis hard problems on expander graphs"
    - "improved bounds for randomly sampling colorings via linear programming"
    - "bis hardness for 2 spin systems on bipartite bounded degree graphs in the tree non uniqueness region"
    - "inapproximability of the partition function for the antiferromagnetic ising and hard core models"
    - "an fptas for counting proper four colorings on cubic graphs"
    - "fptas for bis with degree bounds on one side"
    - "the expressibility of functions on the boolean domain with applications to counting csps"
    - "approximating the partition function of the ferromagnetic potts model"

Connected through hyperedge HE-3 (induced by source paper "statistical physics approaches to unique games"):
  with members:
    - "a deterministic algorithm for counting colorings with 2 delta colors"
    - "deterministic search for cnf satisfying assignments in almost polynomial time"
    - "algorithmic pirogov sinai theory"
    - "computing the number of induced copies of a fixed graph in a bounded degree graph"
    - "mixing of the glauber dynamics for the ferromagnetic potts model"
    - "spectral algorithms for unique games"
    - "how to play unique games on expanders"

Connected through hyperedge HE-4 (induced by source paper "fpras for the potts model and the number of k colorings"):
  with members:
    - "improved bounds for randomly sampling colorings via linear programming"
    - "an fptas for counting proper four colorings on cubic graphs"
    - "mixing of the glauber dynamics for the ferromagnetic potts model"
    - "inapproximability of the tutte polynomial of a planar graph"
    - "approximating the partition function of the ferromagnetic potts model"

Connected through hyperedge HE-5 (induced by source paper "algorithms for bis hard problems on expander graphs"):
  with members:
    - "markov chains for the hard core model via polymer models"
    - "counting independent sets and colorings on random regular bipartite graphs"
    - "sampling in uniqueness from the potts and random cluster models on random regular graphs"
    - "algorithmic pirogov sinai theory"
    - "bis hardness for 2 spin systems on bipartite bounded degree graphs in the tree non uniqueness region"
    - "convergence of mcmc and loopy bp in the tree uniqueness region for the hard core model"
    - "inapproximability of the partition function for the antiferromagnetic ising and hard core models"
    - "random cluster dynamics for the ising model is rapidly mixing"

Connected through hyperedge HE-6 (induced by source paper "algorithmic pirogov sinai theory"):
  with members:
    - "algorithms for bis hard problems on expander graphs"
    - "the ising partition function zeros and deterministic approximation"
    - "inapproximability of the independent set polynomial in the complex plane"
    - "computing the number of induced copies of a fixed graph in a bounded degree graph"
    - "bis hardness for 2 spin systems on bipartite bounded degree graphs in the tree non uniqueness region"
    - "inapproximability of the partition function for the antiferromagnetic ising and hard core models"
    - "random cluster dynamics for the ising model is rapidly mixing"
    - "computing the independence polynomial from the tree threshold down to the roots"

Connected through hyperedge HE-7 (induced by source paper "sampling in uniqueness from the potts and random cluster models on random regular graphs"):
  with members:
    - "algorithms for bis hard problems on expander graphs"
    - "algorithmic pirogov sinai theory"
    - "sampling random colorings of sparse random graphs"
    - "spatial mixing and the connective constant optimal bounds"
    - "mixing of the glauber dynamics for the ferromagnetic potts model"
    - "spatial mixing and approximation algorithms for graphs with bounded connective constant"
    - "approximating partition functions of two state spin systems"

Connected through hyperedge HE-8 (induced by source paper "the complexity of approximately counting retractions"):
  with members:
    - "surjective h colouring new hardness results"
    - "a dichotomy theorem for nonuniform csps"
    - "approximately counting h colourings is bis hard"
    - "the complexity of approximately counting tree homomorphisms"
    - "the complexity of surjective homomorphism problems a survey"
    - "an approximation trichotomy for boolean csp"

Question: Please tell me which class the center node 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)