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 minimum cost connected t joins"):
  Abstract: We design and analyse approximation algorithms for the minimum-cost connected T-join problem: given an undirected graph G = (V;E) with nonnegative costs on the edges, and a subset of nodes T, find (if it exists) a spanning connected subgraph H of minimum cost such that every node in T has odd degree and every node not in T has even degree; H may have multiple copies of any edge of G. Two well-known special cases are the TSP (|T| = 0) and the s-t path TSP (|T| = 2). Recently, An, Kleinberg, and Shmoys [STOC 2012] improved on the long-standing 5/3-approximation guarantee for the latter problem and presented an algorithm based on LP rounding that achieves an approximation guarantee of (1+sqrt(5))/2 < 1.6181. #R##N#We show that the methods of An et al. extend to the minimum-cost connected T-join problem. They presented a new proof for a 5/3-approximation guarantee for the s-t path TSP; their proof extends easily to the minimum-cost connected T-join problem. Next, we improve on the approximation guarantee of 5/3 by extending their LP-rounding algorithm to get an approximation guarantee of 13/8 = 1.625 for all |T| >= 4. #R##N#Finally, we focus on the prize-collecting version of the problem, and present a primal-dual algorithm that is "Lagrangian multiplier preserving" and that achieves an approximation guarantee 3 - 2/(|T|-1) when |T| >= 4. Our primal-dual algorithm is a generalization of the known primal-dual 2-approximation for the prize-collecting s-t path TSP. Furthermore, we show that our analysis is tight by presenting instances with |T| >= 4 such that the cost of the solution found by the algorithm is exactly 3 - 2/(|T|-1) times the cost of the constructed dual solution.

Includes members:
  Member "eight fifth approximation for the path tsp":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "constant factor approximation algorithms for parity constrained facility location problems")
  Member "shorter tours by nicer ears 7 5 approximation for graphic tsp 3 2 for the path version and 4 3 for two edge connected subgraphs":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "travelling on graphs with small highway dimension")
  Member "improving christofides algorithm for the s t path tsp":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "reducing path tsp to tsp")
  Member "approximating graphic tsp by matchings":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "simple cubic graphs with no short traveling salesman tour")
  Member "13 9 approximation for graphic tsp":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "reducing path tsp to tsp")
  Member "combining approximation algorithms for the prize collecting tsp":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "a unified ptas for prize collecting tsp and steiner tree problem in doubling metrics")

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.DS(Data Structures and Algorithms)