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 "hypergraph markov operators eigenvalues and approximation algorithms"):
  Abstract: The celebrated Cheeger's Inequality \cite{am85,a86} establishes a bound on the expansion of a graph via its spectrum. This inequality is central to a rich spectral theory of graphs, based on studying the eigenvalues and eigenvectors of the adjacency matrix (and other related matrices) of graphs. It has remained open to define a suitable spectral model for hypergraphs whose spectra can be used to estimate various combinatorial properties of the hypergraph. #R##N#In this paper we introduce a new hypergraph Laplacian operator (generalizing the Laplacian matrix of graphs)and study its spectra. We prove a Cheeger-type inequality for hypergraphs, relating the second smallest eigenvalue of this operator to the expansion of the hypergraph. We bound other hypergraph expansion parameters via higher eigenvalues of this operator. We give bounds on the diameter of the hypergraph as a function of the second smallest eigenvalue of the Laplacian operator. The Markov process underlying the Laplacian operator can be viewed as a dispersion process on the vertices of the hypergraph that might be of independent interest. We bound the {\em Mixing-time} of this process as a function of the second smallest eigenvalue of the Laplacian operator. All these results are generalizations of the corresponding results for graphs. #R##N#We show that there can be no linear operator for hypergraphs whose spectra captures hypergraph expansion in a Cheeger-like manner. For any $k$, we give a polynomial time algorithm to compute an approximation to the $k^{th}$ smallest eigenvalue of the operator. We show that this approximation factor is optimal under the SSE hypothesis (introduced by \cite{rs10}) for constant values of $k$. #R##N#Finally, using the factor preserving reduction from vertex expansion in graphs to hypergraph expansion, we show that all our results for hypergraphs extend to vertex expansion in graphs.

Includes members:
  Member "approximation algorithms for hypergraph small set expansion and small set vertex expansion":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "planted models for k way edge and vertex expansion")
  Member "the complexity of approximating vertex expansion":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "planted models for k way edge and vertex expansion")
  Member "approximation algorithm for sparsest k partitioning":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "planted models for k way edge and vertex expansion")
  Member "many sparse cuts via higher eigenvalues":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "planted models for k way edge and vertex expansion")
  Member "min max graph partitioning and small set expansion":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "planted models for k way edge and vertex expansion")
  Member "most tensor problems are np hard":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "provable tensor ring completion")
  Member "random tensors and planted cliques":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "optimal average case reductions to sparse pca from weak assumptions to strong hardness")

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)