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 "a tight analysis of bethe approximation for permanent"):
  Abstract: We prove that the permanent of nonnegative matrices can be deterministically approximated within a factor of $\sqrt{2}^n$ in polynomial time, improving upon the previous deterministic approximations. We show this by proving that the Bethe approximation of the permanent, a quantity computable in polynomial time, is at least as large as the permanent divided by $\sqrt{2}^{n}$. This resolves a conjecture of Gurvits. Our bound is tight, and when combined with previously known inequalities lower bounding the permanent, fully resolves the quality of Bethe approximation for permanent.

Includes members:
  Member "log concave polynomials i entropy and a deterministic approximation algorithm for counting bases of matroids":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "a generalized matrix tree theorem for pfaffian pairs")
  Member "approximate profile maximum likelihood":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "a general framework for symmetric property estimation")
  Member "belief propagation bethe approximation and polynomials":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "gauges loops and polynomials for partition functions of graphical models")
  Member "approximating the permanent of a random matrix with vanishing mean":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "a deterministic algorithm for counting colorings with 2 delta colors")
  Member "a generalization of permanent inequalities and applications in counting and optimization":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "gauges loops and polynomials for partition functions of graphical models")
  Member "nash social welfare matrix permanent and stable polynomials":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "efx exists for three agents")
  Member "the bethe permanent of a nonnegative matrix":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "gauges loops and polynomials for partition functions of graphical models")
  Member "approximating the permanent with fractional belief propagation":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "gauges loops and polynomials for partition functions of graphical models")

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)