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 "optimal bound on the combinatorial complexity of approximating polytopes"):
  Abstract: Convex bodies play a fundamental role in geometric computation, and approximating such bodies is often a key ingredient in the design of efficient algorithms. We consider the question of how to succinctly approximate a multidimensional convex body by a polytope. We are given a convex body $K$ of unit diameter in Euclidean $d$-dimensional space (where $d$ is a constant) along with an error parameter $\varepsilon > 0$. The objective is to determine a polytope of low combinatorial complexity whose Hausdorff distance from $K$ is at most $\varepsilon$. By \emph{combinatorial complexity} we mean the total number of faces of all dimensions of the polytope. In the mid-1970's, a result by Dudley showed that $O(1/\varepsilon^{(d-1)/2})$ facets suffice, and Bronshteyn and Ivanov presented a similar bound on the number of vertices. While both results match known worst-case lower bounds, obtaining a similar upper bound on the total combinatorial complexity has been open for over 40 years. Recently, we made a first step forward towards this objective, obtaining a suboptimal bound. In this paper, we settle this problem with an asymptotically optimal bound of $O(1/\varepsilon^{(d-1)/2})$. #R##N#Our result is based on a new relationship between $\varepsilon$-width caps of a convex body and its polar. Using this relationship, we are able to obtain a volume-sensitive bound on the number of approximating caps that are "essentially different." We achieve our result by combining this with a variant of the witness-collector method and a novel variable-width layered construction.

Includes members:
  Member "approximate convex intersection detection with applications to width and minkowski sums":
    also connected through other hyperedges:
      (none)
  Member "near optimal epsilon kernel construction and related problems":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "epsilon approximations and epsilon nets")
  Member "building efficient and compact data structures for simplicial complexes":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "computing discrete morse complexes from simplicial complexes")
  Member "optimal approximate polytope membership":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "algorithms for deciding membership in polytopes of general dimension")
  Member "on the combinatorial complexity of approximating polytopes":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "optimal approximate polytope membership")

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)