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: "nonlinear dimension reduction via outer bi lipschitz extensions"
  Abstract: We introduce and study the notion of an outer bi-Lipschitz extension of a map between Euclidean spaces. The notion is a natural analogue of the notion of a Lipschitz extension of a Lipschitz map. We show that for every map $f$ there exists an outer bi-Lipschitz extension $f'$ whose distortion is greater than that of $f$ by at most a constant factor. This result can be seen as a counterpart of the classic Kirszbraun theorem for outer bi-Lipschitz extensions. We also study outer bi-Lipschitz extensions of near-isometric maps and show upper and lower bounds for them. Then, we present applications of our results to prioritized and terminal dimension reduction problems. #R##N#* We prove a prioritized variant of the Johnson-Lindenstrauss lemma: given a set of points $X\subset \mathbb{R}^d$ of size $N$ and a permutation ("priority ranking") of $X$, there exists an embedding $f$ of $X$ into $\mathbb{R}^{O(\log N)}$ with distortion $O(\log \log N)$ such that the point of rank $j$ has only $O(\log^{3 + \varepsilon} j)$ non-zero coordinates - more specifically, all but the first $O(\log^{3+\varepsilon} j)$ coordinates are equal to $0$; the distortion of $f$ restricted to the first $j$ points (according to the ranking) is at most $O(\log\log j)$. The result makes a progress towards answering an open question by Elkin, Filtser, and Neiman about prioritized dimension reductions. #R##N#* We prove that given a set $X$ of $N$ points in $\mathbb{R}^d$, there exists a terminal dimension reduction embedding of $\mathbb{R}^d$ into $\mathbb{R}^{d'}$, where $d' = O\left(\frac{\log N}{\varepsilon^4}\right)$, which preserves distances $\|x-y\|$ between points $x\in X$ and $y \in \mathbb{R}^{d}$, up to a multiplicative factor of $1 \pm \varepsilon$. This improves a recent result by Elkin, Filtser, and Neiman. #R##N#The dimension reductions that we obtain are nonlinear, and this nonlinearity is necessary.

Connected through hyperedge HE-1 (induced by source paper "labelings vs embeddings on distributed representations of distances"):
  with members:
    - "lossless prioritized embeddings"
    - "almost optimal distance oracles for planar graphs"
    - "optimal terminal dimensionality reduction in euclidean space"
    - "metric embedding via shortest path decompositions"
    - "ramsey spanning trees and their applications"
    - "on notions of distortion and an almost minimum spanning tree with constant average distortion"
    - "prioritized metric structures and embedding"
    - "distance labeling schemes for trees"

Connected through hyperedge HE-2 (induced by source paper "lossless prioritized embeddings"):
  with members:
    - "near isometric terminal embeddings for doubling metrics"
    - "optimal terminal dimensionality reduction in euclidean space"
    - "metric embedding via shortest path decompositions"
    - "efficient algorithms for constructing very sparse spanners and emulators"
    - "on notions of distortion and an almost minimum spanning tree with constant average distortion"
    - "prioritized metric structures and embedding"
    - "the 4 3 additive spanner exponent is tight"
    - "lower stretch spanning trees"

Connected through hyperedge HE-3 (induced by source paper "approximate nearest neighbor for curves simple efficient and deterministic"):
  with members:
    - "sublinear data structures for short fr echet queries"
    - "optimal terminal dimensionality reduction in euclidean space"
    - "locality sensitive hashing of curves"
    - "on the complexity of range searching among curves"
    - "products of euclidean metrics and applications to proximity questions among curves"
    - "why walking the dog takes time frechet distance has no strongly subquadratic algorithms unless seth fails"
    - "faster retrieval with a two pass dynamic time warping lower bound"

Connected through hyperedge HE-4 (induced by source paper "regression via kirszbraun extension with applications to imitation learning"):
  with members:
    - "an algorithmic perspective on imitation learning"
    - "learning monocular reactive uav control in cluttered natural environments"
    - "efficient regression in metric spaces via approximate lipschitz extension"
    - "a reduction of imitation learning and structured prediction to no regret online learning"
    - "electrical flows laplacian systems and faster approximation of maximum flow in undirected graphs"

Connected through hyperedge HE-5 (induced by source paper "regression via kirszbraun extension"):
  with members:
    - "efficient regression in metric spaces via approximate lipschitz extension"
    - "electrical flows laplacian systems and faster approximation of maximum flow in undirected graphs"
    - "fast construction of nets in low dimensional metrics and their applications"
    - "nearly linear time algorithms for graph partitioning graph sparsification and solving linear systems"

Connected through hyperedge HE-6 (induced by source paper "optimal terminal dimensionality reduction in euclidean space"):
  with members:
    - "optimality of the johnson lindenstrauss lemma"
    - "dimensionality reduction with subgaussian matrices a unified theory"

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)