human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "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.

Connected through hyperedge HE-1 (induced by source paper "smoothed analysis of order types"):
  with members:
    - "smoothed analysis of the art gallery problem"
    - "beyond worst case analysis"
    - "the complexity of drawing a graph in a polygonal region"
    - "intersection graphs of rays and grounded segments"
    - "the complexity of tensor rank"
    - "recognition and complexity of point visibility graphs"
    - "intersection graphs of segments and exists mathbb r"
    - "satisfiability of cross product terms is complete for real nondeterministic polytime blum shub smale machines"

Connected through hyperedge HE-2 (induced by source paper "beyond worst case analysis"):
  with members:
    - "being robust in high dimensions can be practical"
    - "implicit regularization in deep learning"
    - "how to escape saddle points efficiently"
    - "local max cut in smoothed polynomial time"
    - "a nearly tight sum of squares lower bound for the planted clique problem"
    - "understanding deep learning requires rethinking generalization"
    - "how robust are reconstruction thresholds for community detection"
    - "k center clustering under perturbation resilience"

Connected through hyperedge HE-3 (induced by source paper "smoothed analysis of the art gallery problem"):
  with members:
    - "beyond worst case analysis"
    - "the complexity of drawing a graph in a polygonal region"
    - "constant approximation algorithms for guarding simple polygons using vertex guards"
    - "irrational guards are sometimes needed"
    - "intersection graphs of rays and grounded segments"
    - "an approximation algorithm for the art gallery problem"
    - "the continuous 1 5d terrain guarding problem discretization optimal solutions and ptas"
    - "recognition and complexity of point visibility graphs"

Connected through hyperedge HE-4 (induced by source paper "fast algorithms for rank 1 bimatrix games"):
  with members:
    - "constant rank bimatrix games are ppad hard"
    - "rank 1 games with exponentially many nash equilibria"
    - "enumerating the nash equilibria of rank 1 games"
    - "settling the complexity of computing two player nash equilibria"
    - "smoothed analysis of algorithms why the simplex algorithm usually takes polynomial time"

Question: Please tell me which class the center node 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)