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 "computational aspects of the colorful caratheodory theorem"):
  Abstract: Let $P_1,...,P_{d+1} \subset \mathbb{R}^d$ be $d$-dimensional point sets such that the convex hull of each $P_i$ contains the origin. We call the sets $P_i$ color classes, and we think of the points in $P_i$ as having color $i$. A colorful choice is a set with at most one point of each color. The colorful Caratheodory theorem guarantees the existence of a colorful choice whose convex hull contains the origin. So far, the computational complexity of finding such a colorful choice is unknown. #R##N#We approach this problem from two directions. First, we consider approximation algorithms: an $m$-colorful choice is a set that contains at most $m$ points from each color class. We show that for any constant $\varepsilon > 0$, an $\lceil \varepsilon(d+1)\rceil$-colorful choice containing the origin in its convex hull can be found in polynomial time. This notion of approximation has not been studied before, and it is motivated through the applications of the colorful Caratheodory theorem in the literature. In the second part, we present a natural generalization of the colorful Caratheodory problem: in the Nearest Colorful Polytope problem (NCP), we are given sets $P_1,...,P_n \subset \mathbb{R}^d$ that do not necessarily contain the origin in their convex hulls. The goal is to find a colorful choice whose convex hull minimizes the distance to the origin. We show that computing local optima for the NCP problem is PLS-complete, while computing a global optimum is NP-hard.

Includes members:
  Member "the rainbow at the end of the line a ppad formulation of the colorful carath eodory theorem with applications":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "no dimensional tverberg theorems and algorithms")
  Member "colorful linear programming nash equilibrium and pivots":
    also connected through other hyperedges:
      (none)
  Member "approximating tverberg points in linear time for any fixed dimension":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "no dimensional tverberg theorems and algorithms")
  Member "a further generalization of the colourful caratheodory theorem":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "colorful linear programming nash equilibrium and pivots")

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)