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 "swendsen wang dynamics for general graphs in the tree uniqueness region"):
  Abstract: The Swendsen-Wang dynamics is a popular algorithm for sampling from the Gibbs distribution for the ferromagnetic Ising model on a graph $G=(V,E)$. The dynamics is a "global" Markov chain which is conjectured to converge to equilibrium in $O(|V|^{1/4})$ steps for any graph $G$ at any (inverse) temperature $\beta$. It was recently proved by Guo and Jerrum (2017) that the Swendsen-Wang dynamics has polynomial mixing time on any graph at all temperatures, yet there are few results providing $o(|V|)$ upper bounds on its convergence time. #R##N#We prove fast convergence of the Swendsen-Wang dynamics on general graphs in the tree uniqueness region of the ferromagnetic Ising model. In particular, when $\beta < \beta_c(d)$ where $\beta_c(d)$ denotes the uniqueness/non-uniqueness threshold on infinite $d$-regular trees, we prove that the relaxation time (i.e., the inverse spectral gap) of the Swendsen-Wang dynamics is $\Theta(1)$ on any graph of maximum degree $d \geq 3$. Our proof utilizes a version of the Swendsen-Wang dynamics which only updates isolated vertices. We establish that this variant of the Swendsen-Wang dynamics has mixing time $O(\log{|V|})$ and relaxation time $\Theta(1)$ on any graph of maximum degree $d$ for all $\beta < \beta_c(d)$. We believe that this Markov chain may be of independent interest, as it is a monotone Swendsen-Wang type chain. As part of our proofs, we provide modest extensions of the technology of Mossel and Sly (2013) for analyzing mixing times and of the censoring result of Peres and Winkler (2013). Both of these results are for the Glauber dynamics, and we extend them here to general monotone Markov chains. This class of dynamics includes for example the heat-bath block dynamics, for which we obtain new tight mixing time bounds.

Includes members:
  Member "spatial mixing and non local markov chains":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "improved strong spatial mixing for colorings on trees")
  Member "random cluster dynamics for the ising model is rapidly mixing":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "lower bounds for testing graphical models colorings and antiferromagnetic ising models")
  Member "spatial mixing and the connective constant optimal bounds":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "spectral independence in high dimensional expanders and applications to the hardcore model")
  Member "approximation algorithms for two state anti ferromagnetic spin systems on bounded degree graphs":
    also connected through other hyperedges:
      - Hyperedge HE-4 (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-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 "adaptive simulated annealing a near optimal connection between sampling and counting":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "fast sampling and counting k sat solutions in the local lemma regime")

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.DM(Discrete Mathematics)