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: "truly optimal euclidean spanners"
  Abstract: Euclidean spanners are important geometric structures, having found numerous applications over the years. Cornerstone results in this area from the late 80s and early 90s state that for any $d$-dimensional $n$-point Euclidean space, there exists a $(1+\epsilon)$-spanner with $nO(\epsilon^{-d+1})$ edges and lightness $O(\epsilon^{-2d})$. Surprisingly, the fundamental question of whether or not these dependencies on $\epsilon$ and $d$ for small $d$ can be improved has remained elusive, even for $d = 2$. This question naturally arises in any application of Euclidean spanners where precision is a necessity. #R##N#The state-of-the-art bounds $nO(\epsilon^{-d+1})$ and $O(\epsilon^{-2d})$ on the size and lightness of spanners are realized by the {\em greedy} spanner. In 2016, Filtser and Solomon proved that, in low dimensional spaces, the greedy spanner is near-optimal. The question of whether the greedy spanner is truly optimal remained open to date. #R##N#The contribution of this paper is two-fold. We resolve these longstanding questions by nailing down the exact dependencies on $\epsilon$ and $d$ and showing that the greedy spanner is truly optimal. Specifically, for any $d= O(1), \epsilon = \Omega({n}^{-\frac{1}{d-1}})$: #R##N#_ We show that any $(1+\epsilon)$-spanner must have $n \Omega(\epsilon^{-d+1})$ edges, implying that the greedy (and other) spanners achieve the optimal size. #R##N#_ We show that any $(1+\epsilon)$-spanner must have lightness $\Omega(\epsilon^{-d})$, and then improve the upper bound on the lightness of the greedy spanner from $O(\epsilon^{-2d})$ to $O(\epsilon^{-d})$. #R##N#We then complement our negative result for the size of spanners with a rather counterintuitive positive result: Steiner points lead to a quadratic improvement in the size of spanners! Our bound for the size of Steiner spanners is tight as well (up to lower-order terms).

Connected through hyperedge HE-1 (induced by source paper "a ptas for subset tsp in minor free graphs"):
  with members:
    - "greedy spanners are optimal in doubling metrics"
    - "on subexponential parameterized algorithms for steiner tree and directed subset tsp on planar graphs"
    - "minor free graphs have light spanners"
    - "the greedy spanner is existentially optimal"
    - "linear size distance preservers"
    - "graph minors for preserving terminal distances approximately lower and upper bounds"
    - "a light metric spanner"
    - "better distance preservers and additive spanners"

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.CG(Computational Geometry)