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 "iterated decomposition of biased permutations via new bounds on the spectral gap of markov chains"):
  Abstract: The spectral gap of a Markov chain can be bounded by the spectral gaps of constituent "restriction" chains and a "projection" chain, and the strength of such a bound is the content of various decomposition theorems. In this paper, we introduce a new parameter that allows us to improve upon these bounds. We further define a notion of orthogonality between the restriction chains and "complementary" restriction chains. This leads to a new Complementary Decomposition theorem, which does not require analyzing the projection chain. For $\epsilon$-orthogonal chains, this theorem may be iterated $O(1/\epsilon)$ times while only giving away a constant multiplicative factor on the overall spectral gap. As an application, we provide a $1/n$-orthogonal decomposition of the nearest neighbor Markov chain over $k$-class biased monotone permutations on [$n$], as long as the number of particles in each class is at least $C\log n$. This allows us to apply the Complementary Decomposition theorem iteratively $n$ times to prove the first polynomial bound on the spectral gap when $k$ is as large as $\Theta(n/\log n)$. The previous best known bound assumed $k$ was at most a constant.

Includes members:
  Member "rapid mixing of k class biased permutations":
    also connected through other hyperedges:
      (none)
  Member "mixing of permutations by biased transposition":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "rapid mixing of k class biased permutations")

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.DS(Data Structures and Algorithms)