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: "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.

Connected through hyperedge HE-1 (induced by source paper "broadcast congested clique planted cliques and pseudorandom generators"):
  with members:
    - "congested clique algorithms for graph spanners"
    - "optimal lower bounds for distributed and streaming spanning forest computation"
    - "msf and connectivity in limited variants of the congested clique"
    - "a time hierarchy theorem for the local model"
    - "on derandomizing local distributed algorithms"
    - "deterministic subgraph detection in broadcast congest"
    - "towards a complexity theory for the congested clique"
    - "deterministic graph connectivity in the broadcast congested clique"

Connected through hyperedge HE-2 (induced by source paper "computational hardness of certifying bounds on constrained pca problems"):
  with members:
    - "mean field approximation convex hierarchies and the optimality of correlation rounding a unified perspective"
    - "heterogeneous multireference alignment a single pass approach"
    - "community detection in hypergraphs spiked tensor models and sum of squares"
    - "the lov asz theta function for random regular graphs and community detection in the hard regime"
    - "the power of sum of squares for detecting hidden structures"
    - "bayesian estimation from few samples community detection and related problems"
    - "sum of squares lower bounds for refuting any csp"
    - "a nearly tight sum of squares lower bound for the planted clique problem"

Connected through hyperedge HE-3 (induced by source paper "bilu linial stability certified algorithms and the independent set problem"):
  with members:
    - "on euclidean k means clustering with alpha center proximity"
    - "exact algorithms and lower bounds for stable instances of euclidean k means"
    - "perturbation resilient clustering for k center and related problems via lp relaxations"
    - "stability and recovery for independence systems"
    - "lp based robust algorithms for noisy minor free and bounded treewidth graphs"
    - "k center clustering under perturbation resilience"
    - "on the lov asz theta function for independent sets in sparse graphs"
    - "bilu linial stable instances of max cut and minimum multiway cut"

Connected through hyperedge HE-4 (induced by source paper "optimization over the boolean hypercube via sums of nonnegative circuit polynomials"):
  with members:
    - "on the bit complexity of sum of squares proofs"
    - "a nearly tight sum of squares lower bound for the planted clique problem"
    - "on the hardest problem formulations for the 0 1 lasserre hierarchy"
    - "lower bounds on the size of semidefinite programming relaxations"
    - "sum of squares hierarchy lower bounds for symmetric formulations"
    - "sum of squares proofs and the quest toward optimal algorithms"
    - "approximating csps with global cardinality constraints using sdp hierarchies"

Connected through hyperedge HE-5 (induced by source paper "hidden hamiltonian cycle recovery via linear programming"):
  with members:
    - "improved sum of squares lower bounds for hidden clique and hidden submatrix problems"
    - "a semidefinite program for unbalanced multisection in the stochastic block model"
    - "exact recovery in the stochastic block model"
    - "information theory of dna shotgun sequencing"
    - "distributed user profiling via spectral methods"
    - "belief propagation for weighted b matchings on arbitrary graphs and its relation to linear programs with integer solutions"

Connected through hyperedge HE-6 (induced by source paper "found graph data and planted vertex covers"):
  with members:
    - "exact recovery in the stochastic block model"
    - "deltacon a principled massive graph similarity function"
    - "listing all maximal cliques in large sparse real world graphs"

Connected through hyperedge HE-7 (induced by source paper "a nearly tight sum of squares lower bound for the planted clique problem"):
  with members:
    - "improved sum of squares lower bounds for hidden clique and hidden submatrix problems"
    - "sum of squares lower bounds for sparse pca"
    - "sum of squares lower bounds from pairwise independence"
    - "sos and planted clique tight analysis of mpw moments at all degrees and an optimal lower bound at degree four"
    - "dictionary learning and tensor decomposition via the sum of squares method"
    - "sum of squares proofs and the quest toward optimal algorithms"
    - "rounding sum of squares relaxations"
    - "hidden cliques and the certification of the restricted isometry property"

Connected through hyperedge HE-8 (induced by source paper "how well do local algorithms solve semidefinite programs"):
  with members:
    - "a nearly tight sum of squares lower bound for the planted clique problem"
    - "improved sum of squares lower bounds for hidden clique and hidden submatrix problems"
    - "semidefinite programs on sparse random graphs and their application to community detection"
    - "how robust are reconstruction thresholds for community detection"
    - "phase transitions in semisupervised clustering of sparse networks"
    - "exact recovery in the stochastic block model"
    - "multireference alignment using semidefinite programming"
    - "spectral redemption in clustering sparse networks"

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.CC(Computational Complexity)