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 of the independent set polynomial below the shearer threshold"):
  Abstract: We study the problem of approximately evaluating the independent set polynomial of bounded-degree graphs at a point lambda or, equivalently, the problem of approximating the partition function of the hard-core model with activity lambda on graphs G of max degree D. For lambda>0, breakthrough results of Weitz and Sly established a computational transition from easy to hard at lambda_c(D)=(D-1)^(D-1)/(D-2)^D, which coincides with the tree uniqueness phase transition from statistical physics. #R##N#For lambda<0, the evaluation of the independent set polynomial is connected to the conditions of the Lovasz Local Lemma. Shearer identified the threshold lambda*(D)=(D-1)^(D-1)/D^D as the maximum value p such that every family of events with failure probability at most p and whose dependency graph has max degree D has nonempty intersection. Very recently, Patel and Regts, and Harvey et al. have independently designed FPTASes for approximating the partition function whenever |lambda|<lambda*(D). #R##N#Our main result establishes for the first time a computational transition at the Shearer threshold. We show that for all D>=3, for all lambda -lambda*(D), establishes a phase transition for negative activities. In fact, we now have the following picture for the problem of approximating the partition function with activity lambda on graphs G of max degree D. #R##N#(i) For -lambda*(D)<lambda<lambda_c(D), the problem admits an FPTAS. #R##N#(ii) For lambda lambda_c(D), the problem is NP-hard. #R##N#Rather than the tree uniqueness threshold of the positive case, the phase transition for negative activities corresponds to the existence of zeros for the partition function of the tree below -lambda*(D).

Includes members:
  Member "computing the independence polynomial in shearer s region for the lll":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "commutative algorithms approximate the lll distribution")
  Member "approximate counting the lovasz local lemma and inference in graphical models":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "fast sampling and counting k sat solutions in the local lemma regime")
  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 "an algorithmic proof of the lovasz local lemma via resampling oracles":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "extensions of the algorithmic lovasz local lemma")
  Member "the complexity of computing the sign of the tutte polynomial":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "the exact complexity of the tutte polynomial")
  Member "inapproximability of the tutte polynomial of a planar graph":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "fpras for the potts model and the number of k colorings")
  Member "correlation decay up to uniqueness in spin systems":
    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 "computational transition at the uniqueness threshold":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "spectral independence in high dimensional expanders and applications to the hardcore model")

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)