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 "the art gallery problem is exists mathbb r complete"):
  Abstract: We prove that the art gallery problem is equivalent under polynomial time reductions to deciding whether a system of polynomial equations over the real numbers has a solution. The art gallery problem is a classical problem in computational geometry. Given a simple polygon $P$ and an integer $k$, the goal is to decide if there exists a set $G$ of $k$ guards within $P$ such that every point $p\in P$ is seen by at least one guard $g\in G$. Each guard corresponds to a point in the polygon $P$, and we say that a guard $g$ sees a point $p$ if the line segment $pg$ is contained in $P$. #R##N#The art gallery problem has stimulated extensive research in geometry and in algorithms. However, the complexity status of the art gallery problem has not been resolved. It has long been known that the problem is $\text{NP}$-hard, but no one has been able to show that it lies in $\text{NP}$. Recently, the computational geometry community became more aware of the complexity class $\exists \mathbb{R}$. The class $\exists \mathbb{R}$ consists of problems that can be reduced in polynomial time to the problem of deciding whether a system of polynomial equations with integer coefficients and any number of real variables has a solution. It can be easily seen that $\text{NP}\subseteq \exists \mathbb{R}$. We prove that the art gallery problem is $\exists \mathbb{R}$-complete, implying that (1) any system of polynomial equations over the real numbers can be encoded as an instance of the art gallery problem, and (2) the art gallery problem is not in the complexity class $\text{NP}$ unless $\text{NP}=\exists \mathbb{R}$. As a corollary of our construction, we prove that for any real algebraic number $\alpha$ there is an instance of the art gallery problem where one of the coordinates of the guards equals $\alpha$ in any guard set of minimum cardinality. That rules out many geometric approaches to the problem.

Includes members:
  Member "the continuous 1 5d terrain guarding problem discretization optimal solutions and ptas":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "a constant factor approximation algorithm for vertex guarding a wv polygon")
  Member "recognition and complexity of point visibility graphs":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "drawing graphs as spanners")
  Member "engineering art galleries":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "the parameterized complexity of guarding almost convex polygons")
  Member "bounding the radii of balls meeting every connected component of semi algebraic sets":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "dynamic toolbox for etrinv")

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)