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 "sampling in uniqueness from the potts and random cluster models on random regular graphs"):
  Abstract: We consider the problem of sampling from the Potts model on random regular graphs. It is conjectured that sampling is possible when the temperature of the model is in the uniqueness regime of the regular tree, but positive algorithmic results have been for the most part elusive. In this paper, for all integers $q\geq 3$ and $\Delta\geq 3$, we develop algorithms that produce samples within error $o(1)$ from the $q$-state Potts model on random $\Delta$-regular graphs, whenever the temperature is in uniqueness, for both the ferromagnetic and antiferromagnetic cases. #R##N#The algorithm for the antiferromagnetic Potts model is based on iteratively adding the edges of the graph and resampling a bichromatic class that contains the endpoints of the newly added edge. Key to the algorithm is how to perform the resampling step efficiently since bichromatic classes may induce linear-sized components. To this end, we exploit the tree uniqueness to show that the average growth of bichromatic components is typically small, which allows us to use correlation decay algorithms for the resampling step. While the precise uniqueness threshold on the tree is not known for general values of $q$ and $\Delta$ in the antiferromagnetic case, our algorithm works throughout uniqueness regardless of its value. #R##N#In the case of the ferromagnetic Potts model, we simplify the algorithm significantly by utilising the random-cluster representation of the model. In particular, we show that a percolation-type algorithm succeeds in sampling from the random-cluster model with parameters $p,q$ on random $\Delta$-regular graphs for all values of $q\geq 1$ and $p<p_c(q,\Delta)$, where $p_c(q,\Delta)$ corresponds to a uniqueness threshold for the model on the $\Delta$-regular tree. When restricted to integer values of $q$, this yields a simplified algorithm for the ferromagnetic Potts model on random $\Delta$-regular graphs.

Includes members:
  Member "algorithms for bis hard problems on expander graphs":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "efficient algorithms for the potts model on small set expanders")
  Member "algorithmic pirogov sinai theory":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "efficient algorithms for the potts model on small set expanders")
  Member "sampling random colorings of sparse random graphs":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "counting solutions to random cnf formulas")
  Member "spatial mixing and the connective constant optimal bounds":
    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 "mixing of the glauber dynamics for the ferromagnetic potts model":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "statistical physics approaches to unique games")
  Member "spatial mixing and approximation algorithms for graphs with bounded connective constant":
    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 "ferromagnetic potts model refined bis hardness and related results":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "efficient algorithms for the potts model on small set expanders")
  Member "approximating partition functions of two state spin systems":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "inapproximability of the partition function for the antiferromagnetic ising and hard core models")

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)