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 "improved bounds for the traveling salesman problem with neighborhoods on uniform disks"):
  Abstract: Given a set of $n$ disks of radius $R$ in the Euclidean plane, the Traveling Salesman Problem With Neighborhoods (TSPN) on uniform disks asks for the shortest tour that visits all of the disks. The problem is a generalization of the classical Traveling Salesman Problem(TSP) on points and has been widely studied in the literature. For the case of disjoint uniform disks of radius $R$, Dumitrescu and Mitchell[2001] show that the optimal TSP tour on the centers of the disks is a $3.547$-approximation to the TSPN version. The core of their analysis is based on bounding the detour that the optimal TSPN tour has to make in order to visit the centers of each disk and shows that it is at most $2Rn$ in the worst case. H\"{a}me, Hyyti\"{a} and Hakula[2011] asked whether this bound is tight when $R$ is small and conjectured that it is at most $\sqrt{3}Rn$. #R##N#We further investigate this question and derive structural properties of the optimal TSPN tour to describe the cases in which the bound is smaller than $2Rn$. Specifically, we show that if the optimal TSPN tour is not a straight line, at least one of the following is guaranteed to be true: the bound is smaller than $1.999Rn$ or the $TSP$ on the centers is a $2$-approximation. The latter bound of $2$ is the best that we can get in general. Our framework is based on using the optimality of the TSPN tour to identify local structures for which the detour is large and then using their geometry to derive better lower bounds on the length of the TSPN tour. This leads to an improved approximation factor of $3.53$ for disjoint uniform disks and $6.728$ for the general case. We further show that the H\"{a}me, Hyyti\"{a} and Hakula conjecture is true for the case of three disks and discuss the method used to obtain it. Along the way, we will uncover one way in which the TSPN problem is structurally different from the classical TSP.

Includes members:
  Member "constant factor approximation for tsp with disks":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "the traveling salesman problem for lines balls and planes")
  Member "a ptas for tsp with neighborhoods among fat regions in the plane":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "a ptas for euclidean tsp with hyperplane neighborhoods")
  Member "the traveling salesman problem for lines balls and planes":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "a ptas for euclidean tsp with hyperplane neighborhoods")
  Member "approximation algorithms for tsp with neighborhoods in the plane":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "adaptive view planning for aerial 3d reconstruction")

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)