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 friendly smoothed analysis of the simplex method"):
  Abstract: Explaining the excellent practical performance of the simplex method for linear programming has been a major topic of research for over 50 years. One of the most successful frameworks for understanding the simplex method was given by Spielman and Teng (JACM `04), who the developed the notion of smoothed analysis. Starting from an arbitrary linear program with $d$ variables and $n$ constraints, Spielman and Teng analyzed the expected runtime over random perturbations of the LP (smoothed LP), where variance $\sigma^2$ Gaussian noise is added to the LP data. In particular, they gave a two-stage shadow vertex simplex algorithm which uses an expected $\widetilde{O}(d^{55} n^{86} \sigma^{-30})$ number of simplex pivots to solve the smoothed LP. Their analysis and runtime was substantially improved by Deshpande and Spielman (FOCS `05) and later Vershynin (SICOMP `09). The fastest current algorithm, due to Vershynin, solves the smoothed LP using an expected $O(d^3 \log^7 n \sigma^{-4} + d^9\log^7 n)$ number of pivots, improving the dependence on $n$ from polynomial to logarithmic. #R##N#While the original proof of Spielman and Teng has now been substantially simplified, the resulting analyses are still quite long and complex and the parameter dependencies far from optimal. In this work, we make substantial progress on this front, providing an improved and simpler analysis of shadow simplex methods, where our main algorithm requires an expected \[ O(d^2 \sqrt{\log n} \sigma^{-2} + d^5 \log^{3/2} n) \] number of simplex pivots. We obtain our results via an improved \emph{shadow bound}, key to earlier analyses as well, combined with algorithmic techniques of Borgwardt (ZOR `82) and Vershynin. As an added bonus, our analysis is completely \emph{modular}, allowing us to obtain non-trivial bounds for perturbations beyond Gaussians, such as Laplace perturbations.

Includes members:
  Member "smoothed analysis of the successive shortest path algorithm":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "modeling and solving a vehicle sharing problem")
  Member "on the shadow simplex method for curved polyhedra":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "geometric random edge")
  Member "geometric random edge":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "extended formulations for stable set polytopes of graphs without two disjoint odd cycles")
  Member "solving totally unimodular lps with the shadow vertex algorithm":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "geometric random edge")
  Member "the simplex method is strongly polynomial for deterministic markov decision processes":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "toward solving 2 tbsg efficiently")
  Member "beyond hirsch conjecture walks on random polytopes and smoothed complexity of the simplex method":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "on the shadow simplex method for curved polyhedra")
  Member "smoothed analysis of the condition numbers and growth factors of matrices":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "on the distance between two neural networks and the stability of learning")
  Member "smoothed analysis of algorithms why the simplex algorithm usually takes polynomial time":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "improper learning for non stochastic control")

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)