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 integrality gap upper bounds for tsp with distances one and two"):
  Abstract: We study the structure of solutions to linear programming formulations for the traveling salesperson problem (TSP). #R##N#We perform a detailed analysis of the support of the subtour elimination linear programming relaxation, which leads to algorithms that find 2-matchings with few components in polynomial time. The number of components directly leads to integrality gap upper bounds for the TSP with distances one and two, for both undirected and directed graphs. #R##N#Our main results concern the subtour elimination relaxation with one additional cutting plane inequality: #R##N#- For undirected instances we obtain an integrality gap upper bound of 5/4 without any further restrictions, of 7/6 if the optimal LP solution is half-integral. #R##N#- For instances of order n where the fractional LP value has a cost of n, we obtain a tight integrality gap upper bound of 10/9 if there is an optimal solution with subcubic support graph. The latter property that the graph is subcubic is implied if the solution is a basic solution in the fractional 2-matching polytope. #R##N#- For directed instances we obtain an integrality gap upper bound of 3/2, and of 4/3 if given an optimal 1/2-integral solution. In the case of undirected graphs, we can avoid to add the cutting plane inequality if we accept slightly increased values. For the tight result, the cutting plane is not required. #R##N#Additionally, we show that relying on the structure of the support is not an artefact of our algorithm, but is necessary under standard complexity-theoretic assumptions: we show that finding improved solutions via local search is W[1]-hard for k-edge change neighborhoods even for the TSP with distances one and two, which strengthens a result of D\'aniel Marx.

Includes members:
  Member "new inapproximability bounds for tsp":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "a quasi polynomial algorithm for well spaced hyperbolic tsp")
  Member "on approximation lower bounds for tsp with bounded metrics":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "characterizing the integrality gap of the subtour lp for the circulant traveling salesman problem")

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)