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 "a simple algorithm for sampling colourings of g n d n up to gibbs uniqueness threshold"):
  Abstract: Approximate random $k$-colouring of a graph $G$ is a well studied problem in computer science and statistical physics. It amounts to constructing a $k$-colouring of $G$ which is distributed close to {\em Gibbs distribution} in polynomial time. Here, we deal with the problem when the underlying graph is an instance of Erd\H{o}s-R\'enyi random graph $G(n,d/n)$, where $d$ is a sufficiently large constant. #R##N#We propose a novel efficient algorithm for approximate random $k$-colouring $G(n,d/n)$ for any $k\geq (1+\epsilon)d$. To be more specific, with probability at least $1-n^{-\Omega(1)}$ over the input instances $G(n,d/n)$ and for $k\geq (1+\epsilon)d$, the algorithm returns a $k$-colouring which is distributed within total variation distance $n^{-\Omega(1)}$ from the Gibbs distribution of the input graph instance. #R##N#The algorithm we propose is neither a MCMC one nor inspired by the message passing algorithms proposed by statistical physicists. Roughly the idea is as follows: Initially we remove sufficiently many edges of the input graph. This results in a "simple graph" which can be $k$-coloured randomly efficiently. The algorithm colours randomly this simple graph. Then it puts back the removed edges one by one. Every time a new edge is put back the algorithm updates the colouring of the graph so that the colouring remains random. #R##N#The performance of the algorithm depends heavily on certain spatial correlation decay properties of the Gibbs distribution.

Includes members:
  Member "sampling colorings almost uniformly in sparse random graphs":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "reconstruction non reconstruction thresholds for colourings of general galton watson trees")
  Member "mcmc sampling colourings and independent sets of g n d n near the uniqueness threshold":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "sampling random colorings of sparse random graphs")

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)