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 "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).

Includes members:
  Member "on the spanning and routing ratio of theta four":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "maximum matchings and minimum blocking sets in θ 6 graphs")
  Member "odd yao yao graphs are not spanners":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "spanning properties of theta theta 6")
  Member "greedy spanners are optimal in doubling metrics":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "distributed construction of light networks")
  Member "minor free graphs have light spanners":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "graph spanners a tutorial review")
  Member "the greedy spanner is existentially optimal":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "a polynomial time algorithm for almost optimal vertex fault tolerant spanners")
  Member "almost all even yao yao graphs are spanners":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "spanning properties of theta theta 6")
  Member "a light metric spanner":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "on the edge crossings of the greedy spanner")
  Member "upper bounds on the spanning ratio of constrained theta graphs":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "routing on the visibility graph")

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.CG(Computational Geometry)