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 "improving christofides algorithm for the s t path tsp"):
  Abstract: We present a deterministic (1+sqrt(5))/2-approximation algorithm for the s-t path TSP for an arbitrary metric. Given a symmetric metric cost on n vertices including two prespecified endpoints, the problem is to find a shortest Hamiltonian path between the two endpoints; Hoogeveen showed that the natural variant of Christofides' algorithm is a 5/3-approximation algorithm for this problem, and this asymptotically tight bound in fact has been the best approximation ratio known until now. We modify this algorithm so that it chooses the initial spanning tree based on an optimal solution to the Held-Karp relaxation rather than a minimum spanning tree; we prove this simple but crucial modification leads to an improved approximation ratio, surpassing the 20-year-old barrier set by the natural Christofides' algorithm variant. Our algorithm also proves an upper bound of (1+sqrt(5))/2 on the integrality gap of the path-variant Held-Karp relaxation. The techniques devised in this paper can be applied to other optimization problems as well: these applications include improved approximation algorithms and improved LP integrality gap upper bounds for the prize-collecting s-t path problem and the unit-weight graphical metric s-t path TSP.

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 "approximating minimum cost connected t joins":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "constant factor approximation algorithms for parity constrained facility location problems")
  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)