human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "sketching and embedding are equivalent for norms"
  Abstract: An outstanding open question (Question #5, this http URL) asks to characterize metric spaces in which distances can be estimated using efficient sketches. Specifically, we say that a sketching algorithm is efficient if it achieves constant approximation using constant sketch size. A well-known result of Indyk (J. ACM, 2006) implies that a metric that admits a constant-distortion embedding into $\ell_p$ for $p\in(0,2]$ also admits an efficient sketching scheme. But is the converse true, i.e., is embedding into $\ell_p$ the only way to achieve efficient sketching? #R##N#We address these questions for the important special case of normed spaces, by providing an almost complete characterization of sketching in terms of embeddings. In particular, we prove that a finite-dimensional normed space allows efficient sketches if and only if it embeds (linearly) into $\ell_{1-\varepsilon}$ with constant distortion. We further prove that for norms that are closed under sum-product, efficient sketching is equivalent to embedding into $\ell_1$ with constant distortion. Examples of such norms include the Earth Mover's Distance (specifically its norm variant, called Kantorovich-Rubinstein norm), and the trace norm (a.k.a. Schatten $1$-norm or the nuclear norm). Using known non-embeddability theorems for these norms by Naor and Schechtman (SICOMP, 2007) and by Pisier (Compositio. Math., 1978), we then conclude that these spaces do not admit efficient sketches either, making progress towards answering another open question (Question #7, this http URL). #R##N#Finally, we observe that resolving whether "sketching is equivalent to embedding into $\ell_1$ for general norms" (i.e., without the above restriction) is equivalent to resolving a well-known open problem in Functional Analysis posed by Kwapien in 1969.

Connected through hyperedge HE-1 (induced by source paper "randomized smoothing of all shapes and sizes"):
  with members:
    - "curse of dimensionality on randomized smoothing for certifiable robustness"
    - "macer attack free and scalable robust training via maximizing certified radius"
    - "robustness certificates for sparse adversarial attacks by randomized ablation"
    - "certified adversarial robustness via randomized smoothing"
    - "wasserstein smoothing certified robustness against wasserstein adversarial attacks"
    - "a convex relaxation barrier to tight robustness verification of neural networks"
    - "scaling provable adversarial defenses"
    - "on the effectiveness of interval bound propagation for training verifiably robust models"

Connected through hyperedge HE-2 (induced by source paper "scalable nearest neighbor search for optimal transport"):
  with members:
    - "hierarchical optimal transport for document representation"
    - "scalable fair clustering"
    - "approximate nearest neighbor search in high dimensions"
    - "practical data dependent metric compression with provable guarantees"
    - "distributed representations of words and phrases and their compositionality"
    - "ramsey partitions and proximity data structures"
    - "planar earthmover is not in l_1"

Connected through hyperedge HE-3 (induced by source paper "nonlinear dimension reduction via outer bi lipschitz extensions"):
  with members:
    - "optimal terminal dimensionality reduction in euclidean space"
    - "optimality of the johnson lindenstrauss lemma"
    - "approximate near neighbors for general symmetric norms"
    - "prioritized metric structures and embedding"
    - "constant factor approximation for balanced cut in the pie model"
    - "the johnson lindenstrauss lemma is optimal for linear dimensionality reduction"
    - "metric extension operators vertex sparsifiers and lipschitz extendability"
    - "ramsey type theorems for metric spaces with applications to online problems"

Connected through hyperedge HE-4 (induced by source paper "spectrum approximation beyond fast matrix multiplication algorithms and hardness"):
  with members:
    - "fast estimation of approximate matrix ranks using spectral densities"
    - "improved rectangular matrix multiplication using powers of the coppersmith winograd tensor"
    - "embeddings of schatten norms with applications to data streams"
    - "improved stochastic trace estimation using mutually unbiased bases"
    - "weighted schatten p norm minimization for image denoising and background subtraction"
    - "sketches for matrix norms faster smaller and more general"
    - "solving ridge regression using sketched preconditioned svrg"
    - "faster eigenvector computation via shift and invert preconditioning"

Connected through hyperedge HE-5 (induced by source paper "on approximating functions of the singular values in a stream"):
  with members:
    - "streaming space complexity of nearly all functions of one variable on frequency vectors"
    - "spectrum estimation from samples"
    - "sublinear estimation of weighted matchings in dynamic data streams"
    - "taylor polynomial estimator for estimating frequency moments"
    - "universal sketches for the frequency negative moments and other decreasing streaming sums"
    - "sketching as a tool for numerical linear algebra"
    - "streaming sums in sublinear space"
    - "optimal error of query sets under the differentially private matrix mechanism"

Connected through hyperedge HE-6 (induced by source paper "sketches for matrix norms faster smaller and more general"):
  with members:
    - "embeddings of schatten norms with applications to data streams"
    - "how to fake multiply by a gaussian matrix"
    - "spectrum estimation from samples"
    - "on approximating functions of the singular values in a stream"
    - "distributed estimation of generalized matrix rank efficient algorithms and lower bounds"
    - "optimal approximate matrix product in terms of stable rank"
    - "streaming symmetric norms via measure concentration"
    - "sketching cuts in graphs and hypergraphs"

Connected through hyperedge HE-7 (induced by source paper "on the complexity of inner product similarity join"):
  with members:
    - "a faster subquadratic algorithm for finding outlier correlations"
    - "practical and optimal lsh for angular distance"
    - "optimal data dependent hashing for approximate near neighbors"
    - "i o efficient similarity join"
    - "probabilistic polynomials and hamming nearest neighbors"
    - "sketching as a tool for numerical linear algebra"
    - "the johnson lindenstrauss lemma is optimal for linear dimensionality reduction"
    - "efficient distributed locality sensitive hashing"

Connected through hyperedge HE-8 (induced by source paper "approximate near neighbors for general symmetric norms"):
  with members:
    - "optimal hashing based time space trade offs for approximate near neighbors"
    - "learning to hash for indexing big data a survey"
    - "approximate nearest neighbor search for ell_p spaces 2 p infty via embeddings"
    - "streaming symmetric norms via measure concentration"
    - "optimal data dependent hashing for approximate near neighbors"
    - "hashing for similarity search a survey"
    - "a directed isoperimetric inequality with application to bregman near neighbor lower bounds"
    - "a unified framework for linear dimensionality reduction in l1"

Question: Please tell me which class the center node 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)