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 "sum of squares lower bounds for planted clique"):
  Abstract: Finding cliques in random graphs and the closely related "planted" clique variant, where a clique of size k is planted in a random G(n, 1/2) graph, have been the focus of substantial study in algorithm design. Despite much effort, the best known polynomial-time algorithms only solve the problem for k ~ sqrt(n). #R##N#In this paper we study the complexity of the planted clique problem under algorithms from the Sum-of-squares hierarchy. We prove the first average case lower bound for this model: for almost all graphs in G(n,1/2), r rounds of the SOS hierarchy cannot find a planted k-clique unless k > n^{1/2r} (up to logarithmic factors). Thus, for any constant number of rounds planted cliques of size n^{o(1)} cannot be found by this powerful class of algorithms. This is shown via an integrability gap for the natural formulation of maximum clique problem on random graphs for SOS and Lasserre hierarchies, which in turn follow from degree lower bounds for the Positivestellensatz proof system. #R##N#We follow the usual recipe for such proofs. First, we introduce a natural "dual certificate" (also known as a "vector-solution" or "pseudo-expectation") for the given system of polynomial equations representing the problem for every fixed input graph. Then we show that the matrix associated with this dual certificate is PSD (positive semi-definite) with high probability over the choice of the input graph.This requires the use of certain tools. One is the theory of association schemes, and in particular the eigenspaces and eigenvalues of the Johnson scheme. Another is a combinatorial method we develop to compute (via traces) norm bounds for certain random matrices whose entries are highly dependent; we hope this method will be useful elsewhere.

Includes members:
  Member "improved sum of squares lower bounds for hidden clique and hidden submatrix problems":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "broadcast congested clique planted cliques and pseudorandom generators")
  Member "association schemes non commutative polynomial concentration and sum of squares lower bounds for planted clique":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "fast spectral algorithms from sum of squares proofs tensor decomposition and planted sparse vectors")
  Member "hypercontractivity sum of squares proofs and their applications":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "sum of squares bounds for the ordering principle")
  Member "approximability and proof complexity":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "efficiently learning structured distributions from untrusted batches")
  Member "rounding semidefinite programming hierarchies via global correlation":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "new dependencies of hierarchies in polynomial optimization")
  Member "polynomial integrality gaps for strong sdp relaxations of densest k subgraph":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "high dimensional estimation via sum of squares proofs")

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.CC(Computational Complexity)