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 "eight fifth approximation for the path tsp"):
  Abstract: We prove the approximation ratio 8/5 for the metric {s,t}-path-TSP, and more generally for shortest connected T-joins.#R##N##R##N#The algorithm that achieves this ratio is the simple "Best of Many" version of Christofides' algorithm (1976), suggested by An, Kleinberg and Shmoys (2012), which consists in determining the best Christofides {s,t}-tour out of those constructed from a family $\mathcal{F}_+$ of trees having a convex combination dominated by an optimal solution x* of the Held-Karp relaxation. They give the approximation guarantee $\frac{\sqrt{5}+1}{2}$ for such an {s,t}-tour, which is the first improvement after the 5/3 guarantee of Hoogeveen's Christofides type algorithm (1991). Cheriyan, Friggstad and Gao (2012) extended this result to a 13/8-approximation of shortest connected T-joins, for |T|≥4.#R##N##R##N#The ratio 8/5 is proved by simplifying and improving the approach of An, Kleinberg and Shmoys that consists in completing x*/2 in order to dominate the cost of "parity correction" for spanning trees. We partition the edge-set of each spanning tree in $\mathcal{F}_+$ into an {s,t}-path (or more generally, into a T-join) and its complement, which induces a decomposition of x*. This decomposition can be refined and then efficiently used to complete x*/2 without using linear programming or particular properties of T, but by adding to each cut deficient for x*/2 an individually tailored explicitly given vector, inherent in x*.#R##N##R##N#A simple example shows that the Best of Many Christofides algorithm may not find a shorter {s,t}-tour than 3/2 times the incidentally common optima of the problem and of its fractional relaxation.

Includes members:
  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-1 (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-2 (induced by source paper "constant factor approximation algorithms for parity constrained facility location problems")
  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")

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.DM(Discrete Mathematics)