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 "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.

Includes members:
  Member "a nearly tight sum of squares lower bound for the planted clique problem":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "broadcast congested clique planted cliques and pseudorandom generators")
  Member "improved sum of squares lower bounds for hidden clique and hidden submatrix problems":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "broadcast congested clique planted cliques and pseudorandom generators")
  Member "semidefinite programs on sparse random graphs and their application to community detection":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "computational hardness of certifying bounds on constrained pca problems")
  Member "how robust are reconstruction thresholds for community detection":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "improper learning for non stochastic control")
  Member "sum of squares lower bounds for planted clique":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "broadcast congested clique planted cliques and pseudorandom generators")
  Member "phase transitions in semisupervised clustering of sparse networks":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "renyi entropy bounds on the active learning cost performance tradeoff")
  Member "exact recovery in the stochastic block model":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "renyi entropy bounds on the active learning cost performance tradeoff")
  Member "multireference alignment using semidefinite programming":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "synchronisation of partial multi matchings via non negative factorisations")

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.DM(Discrete Mathematics)