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: "how well do local algorithms solve semidefinite programs"
  Abstract: Several probabilistic models from high-dimensional statistics and machine learning reveal an intriguing --and yet poorly understood-- dichotomy. Either simple local algorithms succeed in estimating the object of interest, or even sophisticated semi-definite programming (SDP) relaxations fail. #R##N#In order to explore this phenomenon, we study a classical SDP relaxation of the minimum graph bisection problem, when applied to Erd\H{o}s-Renyi random graphs with bounded average degree $d>1$, and obtain several types of results. First, we use a dual witness construction (using the so-called non-backtracking matrix of the graph) to upper bound the SDP value. Second, we prove that a simple local algorithm approximately solves the SDP to within a factor $2d^2/(2d^2+d-1)$ of the upper bound. In particular, the local algorithm is at most $8/9$ suboptimal, and $1+O(1/d)$ suboptimal for large degree. #R##N#We then analyze a more sophisticated local algorithm, which aggregates information according to the harmonic measure on the limiting Galton-Watson (GW) tree. The resulting lower bound is expressed in terms of the conductance of the GW tree and matches surprisingly well the empirically determined SDP values on large-scale Erd\H{o}s-Renyi graphs. #R##N#We finally consider the planted partition model. In this case, purely local algorithms are known to fail, but they do succeed if a small amount of side information is available. Our results imply quantitative bounds on the threshold for partial recovery using SDP in this model.

Connected through hyperedge HE-1 (induced by source paper "vector colorings of random ramanujan and large girth irregular graphs"):
  with members:
    - "an alon boppana type bound for weighted graphs and lowerbounds for spectral sparsification"
    - "spectral redemption in clustering sparse networks"
    - "community detection thresholds and the weak ramanujan property"
    - "approximate graph coloring by semidefinite programming"

Connected through hyperedge HE-2 (induced by source paper "the power of sum of squares for detecting hidden structures"):
  with members:
    - "exact tensor completion with sum of squares"
    - "a nearly tight sum of squares lower bound for the planted clique problem"
    - "polynomial time tensor decompositions with sum of squares"
    - "multiplicative approximations for polynomial optimization over the unit sphere"
    - "spectral algorithms for tensor completion"
    - "strongly refuting random csps below the spectral threshold"
    - "improved sum of squares lower bounds for hidden clique and hidden submatrix problems"
    - "how to refute a random csp"

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.DM(Discrete Mathematics)