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 "subgraph sparsification and nearly optimal ultrasparsifiers"):
  Abstract: We consider a variation of the spectral sparsification problem where we are required to keep a subgraph of the original graph. Formally, given a union of two weighted graphs $G$ and $W$ and an integer $k$, we are asked to find a $k$-edge weighted graph $W_k$ such that $G+W_k$ is a good spectral sparsifer of $G+W$. We will refer to this problem as the subgraph (spectral) sparsification. We present a nontrivial condition on $G$ and $W$ such that a good sparsifier exists and give a polynomial time algorithm to find the sparsifer. #R##N#%$O(\frac{n}{k})\log n \tilde{O}(\log \log n)$ As a significant application of our technique, we show that for each positive integer $k$, every $n$-vertex weighted graph has an $(n-1+k)$-edge spectral sparsifier with relative condition number at most $\frac{n}{k} \log n \tilde{O}(\log\log n)$ where $\tilde{O}()$ hides lower order terms. Our bound is within a factor of $\tilde{O}(\log \log n)$ from optimal. This nearly settles a question left open by Spielman and Teng about ultrasparsifiers, which is a key component in their nearly linear-time algorithms for solving diagonally dominant symmetric linear systems. #R##N#We also present another application of our technique to spectral optimization in which the goal is to maximize the algebraic connectivity of a graph (e.g. turn it into an expander) with a limited number of edges.

Includes members:
  Member "twice ramanujan sparsifiers":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "sketching transformed matrices with applications to natural language processing")
  Member "spectral sparsification of graphs":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "approximating spectral clustering via sampling a review")
  Member "graph sparsification by effective resistances":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "approximating spectral clustering via sampling a review")
  Member "nearly tight low stretch spanning trees":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "2 node connectivity network design")
  Member "nearly linear time algorithms for preconditioning and solving symmetric diagonally dominant linear systems":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "speeding up linear programming using randomized linear algebra")
  Member "lower stretch spanning trees":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "2 node connectivity network design")
  Member "nearly linear time algorithms for graph partitioning graph sparsification and solving linear systems":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "compressive sensing for cut improvement and local clustering")

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)