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: "metric extension operators vertex sparsifiers and lipschitz extendability"
  Abstract: We study vertex cut and flow sparsifiers that were recently introduced by Moitra, and Leighton and Moitra. We improve and generalize their results. We give a new polynomial-time algorithm for constructing O(log k / log log k) cut and flow sparsifiers, matching the best existential upper bound on the quality of a sparsifier, and improving the previous algorithmic upper bound of O(log^2 k / log log k). We show that flow sparsifiers can be obtained from linear operators approximating minimum metric extensions. We introduce the notion of (linear) metric extension operators, prove that they exist, and give an exact polynomial-time algorithm for finding optimal operators. #R##N#We then establish a direct connection between flow and cut sparsifiers and Lipschitz extendability of maps in Banach spaces, a notion studied in functional analysis since 1930s. Using this connection, we prove a lower bound of Omega(sqrt{log k/log log k}) for flow sparsifiers and a lower bound of Omega(sqrt{log k}/log log k) for cut sparsifiers. We show that if a certain open question posed by Ball in 1992 has a positive answer, then there exist \tilde O(sqrt{log k}) cut sparsifiers. On the other hand, any lower bound on cut sparsifiers better than \tilde Omega(sqrt{log k}) would imply a negative answer to this question.

Connected through hyperedge HE-1 (induced by source paper "scattering and sparse partitions and their applications"):
  with members:
    - "lossless prioritized embeddings"
    - "labelings vs embeddings on distributed representations of distances"
    - "on strong diameter padded decompositions"
    - "a face cover perspective to ell_1 embeddings of planar graphs"
    - "flow cut gaps and face covers in planar graphs"
    - "near isometric terminal embeddings for doubling metrics"
    - "light spanners for high dimensional norms via stochastic decompositions"
    - "steiner point removal with distortion o log k"

Connected through hyperedge HE-2 (induced by source paper "fully dynamic spectral vertex sparsifiers and applications"):
  with members:
    - "dynamic low stretch trees via dynamic low diameter decompositions"
    - "graph reduction by local variation"
    - "kirchhoff index as a measure of edge centrality in weighted networks nearly linear time algorithms"
    - "dynamic effective resistances and approximate schur complement on separable graphs"
    - "on solving linear systems in sublinear time"
    - "spectrally approximating large graphs with smaller graphs"
    - "an almost linear time algorithm for uniform random spanning tree generation"
    - "density independent algorithms for sparsifying k step random walks"

Connected through hyperedge HE-3 (induced by source paper "vertex sparsifiers for c edge connectivity"):
  with members:
    - "a faster local algorithm for detecting bounded size cuts with applications to higher connectivity problems"
    - "fully dynamic spectral vertex sparsifiers and applications"
    - "breaking quadratic time for small vertex connectivity and an approximation scheme"
    - "dynamic effective resistances and approximate schur complement on separable graphs"
    - "expander decomposition and pruning faster stronger and simpler"
    - "improved guarantees for vertex sparsification in planar graphs"
    - "the power of vertex sparsifiers in dynamic graph algorithms"
    - "sampling random spanning trees faster than matrix multiplication"

Connected through hyperedge HE-4 (induced by source paper "on communication complexity of fixed point computation"):
  with members:
    - "complexity theory game theory and economics"
    - "near optimal communication lower bounds for approximate nash equilibria"
    - "settling the complexity of computing approximate two player nash equilibria"
    - "communication complexity of approximate nash equilibria"
    - "inapproximability of nash equilibrium"
    - "communication lower bounds via critical block sensitivity"
    - "query complexity of approximate nash equilibria"
    - "tight bounds for lp samplers finding duplicates in streams and related problems"

Connected through hyperedge HE-5 (induced by source paper "spectral subspace sparsification"):
  with members:
    - "dynamic effective resistances and approximate schur complement on separable graphs"
    - "an almost linear time algorithm for uniform random spanning tree generation"
    - "improved guarantees for vertex sparsification in planar graphs"
    - "determinant preserving sparsification of sddm matrices with applications to counting and sampling spanning trees"
    - "sampling random spanning trees faster than matrix multiplication"
    - "graph minors for preserving terminal distances approximately lower and upper bounds"
    - "approximate gaussian elimination for laplacians fast sparse and simple"
    - "vertex sparsifiers new results from old techniques"

Connected through hyperedge HE-6 (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"
    - "sketching and embedding are equivalent for norms"
    - "constant factor approximation for balanced cut in the pie model"
    - "the johnson lindenstrauss lemma is optimal for linear dimensionality reduction"
    - "ramsey type theorems for metric spaces with applications to online problems"

Connected through hyperedge HE-7 (induced by source paper "refined vertex sparsifiers of planar graphs"):
  with members:
    - "relaxed voronoi a simple framework for terminal clustering problems"
    - "steiner point removal with distortion o log k"
    - "improved guarantees for vertex sparsification in planar graphs"
    - "an exponential lower bound for cut sparsifiers in planar graphs"
    - "steiner point removal distant terminals don t really bother"
    - "graph minors for preserving terminal distances approximately lower and upper bounds"
    - "vertex sparsifiers new results from old techniques"
    - "on vertex sparsifiers with steiner nodes"

Connected through hyperedge HE-8 (induced by source paper "an exponential lower bound for cut sparsifiers in planar graphs"):
  with members:
    - "improved guarantees for vertex sparsification in planar graphs"
    - "vertex sparsifiers new results from old techniques"
    - "flows in one crossing minor free graphs"
    - "on vertex sparsifiers with steiner nodes"
    - "mimicking networks and succinct representations of terminal cuts"
    - "representative sets and irrelevant vertices new tools for kernelization"

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)