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 "tight bounds for ell_p oblivious subspace embeddings"):
  Abstract: An $\ell_p$ oblivious subspace embedding is a distribution over $r \times n$ matrices $\Pi$ such that for any fixed $n \times d$ matrix $A$, $$\Pr_{\Pi}[\textrm{for all }x, \ \|Ax\|_p \leq \|\Pi Ax\|_p \leq \kappa \|Ax\|_p] \geq 9/10,$$ where $r$ is the dimension of the embedding, $\kappa$ is the distortion of the embedding, and for an $n$-dimensional vector $y$, $\|y\|_p$ is the $\ell_p$-norm. Another important property is the sparsity of $\Pi$, that is, the maximum number of non-zero entries per column, as this determines the running time of computing $\Pi \cdot A$. While for $p = 2$ there are nearly optimal tradeoffs in terms of the dimension, distortion, and sparisty, for the important case of $1 \leq p < 2$, much less was known. In this paper we obtain nearly optimal tradeoffs for $\ell_p$ oblivious subspace embeddings for every $1 \leq p < 2$. #R##N#We show for every $1 \leq p < 2$, any oblivious subspace embedding with dimension $r$ has distortion $\kappa = \Omega \left(\frac{1}{\left(\frac{1}{d}\right)^{1 / p} \cdot \log^{2 / p}r + \left(\frac{r}{n}\right)^{1 / p - 1 / 2}}\right).$ When $r = \mathrm{poly}(d)$ in applications, this gives a $\kappa = \Omega(d^{1/p}\log^{-2/p} d)$ lower bound, and shows the oblivious subspace embedding of Sohler and Woodruff (STOC, 2011) for $p = 1$ and the oblivious subspace embedding of Meng and Mahoney (STOC, 2013) for $1 < p < 2$ are optimal up to $\mathrm{poly}(\log(d))$ factors. We also give sparse oblivious subspace embeddings for every $1 \leq p < 2$ which are optimal in dimension and distortion, up to $\mathrm{poly}(\log d)$ factors. #R##N#Oblivious subspace embeddings are crucial for distributed and streaming environments, as well as entrywise $\ell_p$ low rank approximation. Our results give improved algorithms for these applications.

Includes members:
  Member "uniform sampling for matrix approximation":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "sketching transformed matrices with applications to natural language processing")
  Member "quantile regression for large scale applications":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "efficient symmetric norm regression via linear sketching")
  Member "lower bounds for oblivious subspace embeddings":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "streaming low rank matrix approximation with an application to scientific simulation")
  Member "toward a unified theory of sparse dimensionality reduction in euclidean space":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "robust and sample optimal algorithms for psd low rank approximation")
  Member "low rank approximation and regression in input sparsity time":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "sketching transformed matrices with applications to natural language processing")
  Member "iterative row sampling":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "sketching transformed matrices with applications to natural language processing")
  Member "osnap faster numerical linear algebra algorithms via sparser subspace embeddings":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "sketching transformed matrices with applications to natural language processing")
  Member "the fast cauchy transform and faster robust linear regression":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "optimal sketching for kronecker product regression and low rank approximation")

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)