human: Given a hyperedge-centered hypergraph: <hypergraph>, where the center hyperedge is induced by one source paper and its member nodes are the cited papers.

Details of the hypergraph:
Center hyperedge (induced by source paper "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.

Includes members:
  Member "optimal terminal dimensionality reduction in euclidean space":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "labelings vs embeddings on distributed representations of distances")
  Member "optimality of the johnson lindenstrauss lemma":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "solving tall dense linear programs in nearly linear time")
  Member "approximate near neighbors for general symmetric norms":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "approximate similarity search under edit distance using locality sensitive hashing")
  Member "prioritized metric structures and embedding":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "scattering and sparse partitions and their applications")
  Member "sketching and embedding are equivalent for norms":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "randomized smoothing of all shapes and sizes")
  Member "constant factor approximation for balanced cut in the pie model":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "robust clustering oracle and local reconstructor of cluster structure of graphs")
  Member "the johnson lindenstrauss lemma is optimal for linear dimensionality reduction":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "sub gaussian matrices on sets optimal tail dependence and applications")
  Member "metric extension operators vertex sparsifiers and lipschitz extendability":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "scattering and sparse partitions and their applications")

Question: Please tell me which class the source paper 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)