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: "vertex sparsifiers and abstract rounding algorithms"
  Abstract: The notion of vertex sparsification is introduced in \cite{M}, where it was shown that for any graph $G = (V, E)$ and a subset of $k$ terminals $K \subset V$, there is a polynomial time algorithm to construct a graph $H = (K, E_H)$ on just the terminal set so that simultaneously for all cuts $(A, K-A)$, the value of the minimum cut in $G$ separating $A$ from $K -A$ is approximately the same as the value of the corresponding cut in $H$. #R##N#We give the first super-constant lower bounds for how well a cut-sparsifier $H$ can simultaneously approximate all minimum cuts in $G$. We prove a lower bound of $\Omega(\log^{1/4} k)$ -- this is polynomially-related to the known upper bound of $O(\log k/\log \log k)$. This is an exponential improvement on the $\Omega(\log \log k)$ bound given in \cite{LM} which in fact was for a stronger vertex sparsification guarantee, and did not apply to cut sparsifiers. #R##N#Despite this negative result, we show that for many natural problems, we do not need to incur a multiplicative penalty for our reduction. We obtain optimal $O(\log k)$-competitive Steiner oblivious routing schemes, which generalize the results in \cite{R}. We also demonstrate that for a wide range of graph packing problems (which includes maximum concurrent flow, maximum multiflow and multicast routing, among others, as a special case), the integrality gap of the linear program is always at most $O(\log k)$ times the integrality gap restricted to trees. This result helps to explain the ubiquity of the $O(\log k)$ guarantees for such problems. #R##N#Lastly, we use our ideas to give an efficient construction for vertex-sparsifiers that match the current best existential results -- this was previously open. Our algorithm makes novel use of Earth-mover constraints.

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 "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-5 (induced by source paper "minimizing branching vertices in distance preserving subgraphs"):
  with members:
    - "steiner point removal with distortion o log k"
    - "distance preserving subgraphs of interval graphs"
    - "linear size distance preservers"
    - "vertex sparsifiers new results from old techniques"
    - "preserving terminal distances using minors"
    - "spectral sparsification of graphs"

Connected through hyperedge HE-6 (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-7 (induced by source paper "spectral sparsification and regret minimization beyond matrix multiplicative updates"):
  with members:
    - "sparse sums of positive semidefinite matrices"
    - "using optimization to break the epsilon barrier a faster and simpler width independent algorithm for solving positive linear programs in parallel"
    - "an efficient algorithm for unweighted spectral graph sparsification"
    - "an almost linear time algorithm for approximate max flow in undirected graphs and its multicommodity generalizations"
    - "an efficient parallel solver for sdd linear systems"
    - "near optimal algorithms for online matrix prediction"
    - "a matrix hyperbolic cosine algorithm and applications"
    - "regret analysis of stochastic and nonstochastic multi armed bandit problems"

Connected through hyperedge HE-8 (induced by source paper "dynamic sketching for graph optimization problems with applications to cut preserving sketches"):
  with members:
    - "single pass spectral sparsification in dynamic streams"
    - "on vertex sparsifiers with steiner nodes"
    - "mimicking networks and succinct representations of terminal cuts"
    - "representative sets and irrelevant vertices new tools for kernelization"
    - "compression via matroids a randomized polynomial kernel for odd cycle transversal"

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)