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 "approximating the simplicial depth"):
  Abstract: Let $P$ be a set of $n$ points in $d$-dimensions. The simplicial depth, $\sigma_P(q)$ of a point $q$ is the number of $d$-simplices with vertices in $P$ that contain $q$ in their convex hulls. The simplicial depth is a notion of data depth with many applications in robust statistics and computational geometry. Computing the simplicial depth of a point is known to be a challenging problem. The trivial solution requires $O(n^{d+1})$ time whereas it is generally believed that one cannot do better than $O(n^{d-1})$. In this paper, we consider approximation algorithms for computing the simplicial depth of a point. For $d=2$, we present a new data structure that can approximate the simplicial depth in polylogarithmic time, using polylogarithmic query time. In 3D, we can approximate the simplicial depth of a given point in near-linear time, which is clearly optimal up to polylogarithmic factors. For higher dimensions, we consider two approximation algorithms with different worst-case scenarios. By combining these approaches, we compute a $(1+\varepsilon)$-approximation of the simplicial depth in time $\tilde{O}(n^{d/2 + 1})$ ignoring polylogarithmic factor. All of these algorithms are Monte Carlo algorithms. Furthermore, we present a simple strategy to compute the simplicial depth exactly in $O(n^d \log n)$ time, which provides the first improvement over the trivial $O(n^{d+1})$ time algorithm for $d>4$. Finally, we show that computing the simplicial depth exactly is #P-complete and W[1]-hard if the dimension is part of the input.

Includes members:
  Member "orthogonal range searching on the ram revisited":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "path query data structures in practice")
  Member "deterministic sampling and range counting in geometric data streams":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "the adversarial robustness of sampling")

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)