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: "spectrum approximation beyond fast matrix multiplication algorithms and hardness"
  Abstract: Understanding the singular value spectrum of a matrix $A \in \mathbb{R}^{n \times n}$ is a fundamental task in countless applications. In matrix multiplication time, it is possible to perform a full SVD and directly compute the singular values $\sigma_1,...,\sigma_n$. However, little is known about algorithms that break this runtime barrier. #R##N#Using tools from stochastic trace estimation, polynomial approximation, and fast system solvers, we show how to efficiently isolate different ranges of $A$'s spectrum and approximate the number of singular values in these ranges. We thus effectively compute a histogram of the spectrum, which can stand in for the true singular values in many applications. #R##N#We use this primitive to give the first algorithms for approximating a wide class of symmetric matrix norms in faster than matrix multiplication time. For example, we give a $(1 + \epsilon)$ approximation algorithm for the Schatten-$1$ norm (the nuclear norm) running in just $\tilde O((nnz(A)n^{1/3} + n^2)\epsilon^{-3})$ time for $A$ with uniform row sparsity or $\tilde O(n^{2.18} \epsilon^{-3})$ time for dense matrices. The runtime scales smoothly for general Schatten-$p$ norms, notably becoming $\tilde O (p \cdot nnz(A) \epsilon^{-3})$ for any $p \ge 2$. #R##N#At the same time, we show that the complexity of spectrum approximation is inherently tied to fast matrix multiplication in the small $\epsilon$ regime. We prove that achieving milder $\epsilon$ dependencies in our algorithms would imply faster than matrix multiplication time triangle detection for general graphs. This further implies that highly accurate algorithms running in subcubic time yield subcubic time matrix multiplication. As an application of our bounds, we show that precisely computing all effective resistances in a graph in less than matrix multiplication time is likely difficult, barring a major algorithmic breakthrough.

Connected through hyperedge HE-1 (induced by source paper "schatten norms in matrix streams hello sparsity goodbye dimension"):
  with members:
    - "approximating the spectrum of a graph"
    - "embeddings of schatten norms with applications to data streams"
    - "weighted schatten p norm minimization for image denoising and background subtraction"
    - "estimating the trace of the matrix inverse by interpolating from the diagonal of an approximate inverse"
    - "spectrum estimation from samples"
    - "on approximating functions of the singular values in a stream"
    - "matrix norms in data streams faster multi pass and row order"
    - "a randomized algorithm for approximating the log determinant of a symmetric positive definite matrix"

Connected through hyperedge HE-2 (induced by source paper "graph sparsification spectral sketches and faster resistance computation via short cycle decompositions"):
  with members:
    - "current flow group closeness centrality for complex networks"
    - "massively parallel algorithms for finding well connected components in sparse graphs"
    - "kirchhoff index as a measure of edge centrality in weighted networks nearly linear time algorithms"
    - "fully dynamic effective resistances"
    - "an sdp based algorithm for linear sized spectral sparsification"
    - "an almost linear time algorithm for uniform random spanning tree generation"
    - "nearly tight bounds for sandpile transience on the grid"
    - "optimal lower bounds for sketching graph cuts"

Connected through hyperedge HE-3 (induced by source paper "randomized linear algebra approaches to estimate the von neumann entropy of density matrices"):
  with members:
    - "a randomized algorithm for approximating the log determinant of a symmetric positive definite matrix"
    - "large scale log determinant computation through stochastic chebyshev expansions"
    - "improved bounds on sample size for implicit matrix trace estimators"
    - "low rank approximation and regression in input sparsity time"
    - "osnap faster numerical linear algebra algorithms via sparser subspace embeddings"
    - "low distortion subspace embeddings in input sparsity time and applications to robust linear regression"
    - "sketching and streaming entropy via approximation theory"
    - "faster least squares approximation"

Connected through hyperedge HE-4 (induced by source paper "dynamic effective resistances and approximate schur complement on separable graphs"):
  with members:
    - "fully dynamic effective resistances"
    - "an almost linear time algorithm for uniform random spanning tree generation"
    - "the power of vertex sparsifiers in dynamic graph algorithms"
    - "decremental single source reachability in planar digraphs"
    - "sampling random spanning trees faster than matrix multiplication"
    - "popular conjectures as a barrier for dynamic planar graph algorithms"

Connected through hyperedge HE-5 (induced by source paper "exploiting numerical sparsity for efficient learning faster eigenvector computation and regression"):
  with members:
    - "faster eigenvector computation via shift and invert preconditioning"
    - "randomized block krylov methods for stronger and faster approximate singular value decomposition"
    - "a stochastic pca and svd algorithm with an exponential convergence rate"
    - "a note on randomized element wise matrix sparsification"
    - "near optimal entrywise sampling for data matrices"

Connected through hyperedge HE-6 (induced by source paper "approximations of schatten norms via taylor expansions"):
  with members:
    - "a randomized algorithm for approximating the log determinant of a symmetric positive definite matrix"
    - "improved bounds on sample size for implicit matrix trace estimators"

Connected through hyperedge HE-7 (induced by source paper "stability of the lanczos method for matrix function approximation"):
  with members:
    - "lazysvd even faster svd decomposition yet without agonizing pain"
    - "faster algorithms for computing the stationary distribution simulating random walks and more"
    - "principal component projection without principal component analysis"
    - "randomized block krylov methods for stronger and faster approximate singular value decomposition"
    - "large scale log determinant computation through stochastic chebyshev expansions"
    - "the noisy power method a meta algorithm with applications"
    - "approximating the exponential the lanczos method and an tilde o m time spectral algorithm for balanced separator"
    - "a note on preconditioning by low stretch spanning trees"

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)