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 "colored stochastic dominance problems"):
  Abstract: In this paper, we study the dominance relation under a stochastic setting. Let $\mathcal{S}$ be a set of $n$ colored stochastic points in $\mathbb{R}^d$, each of which is associated with an existence probability. We investigate the problem of computing the probability that a realization of $\mathcal{S}$ contains inter-color dominances, which we call the \textit{colored stochastic dominance} (CSD) problem. We propose the first algorithm to solve the CSD problem for $d=2$ in $O(n^2 \log^2 n)$ time. On the other hand, we prove that, for $d \geq 3$, even the CSD problem with a restricted color pattern is \#P-hard. In addition, even if the existence probabilities are restricted to be $\frac{1}{2}$, the problem remains \#P-hard for $d \geq 7$. A simple FPRAS is then provided to approximate the desired probability in any dimension. We also study a variant of the CSD problem in which the dominance relation is considered with respect to not only the standard basis but any orthogonal basis of $\mathbb{R}^d$. Specifically, this variant, which we call the {\em free-basis colored stochastic dominance} (FBCSD) problem, considers the probability that a realization of $\mathcal{S}$ contains inter-color dominances with respect to any orthogonal basis of $\mathbb{R}^d$. We show that the CSD problem is polynomial-time reducible to the FBCSD problem in the same dimension, which proves the \#P-hardness of the latter for $d \geq 3$. Conversely, we reduce the FBCSD problem in $\mathbb{R}^2$ to the CSD problem in $\mathbb{R}^2$, by which an $O(n^4 \log^2 n)$ time algorithm for the former is obtained.

Includes members:
  Member "nearest neighbor searching under uncertainty ii":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "updating dynamic random hyperbolic graphs in sublinear time")
  Member "convex hulls under uncertainty":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "computing shapley values for mean width in 3 d")

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)