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 "vector colorings of random ramanujan and large girth irregular graphs"):
  Abstract: We prove that in sparse Erdős-Renyi graphs of average degree $d$, the vector chromatic number (the relaxation of chromatic number coming from the Lovasz theta function) is typically $\tfrac{1}{2}\sqrt{d} + o_d(1)$. This fits with a long-standing conjecture that various refutation and hypothesis-testing problems concerning $k$-colorings of sparse Erdős-Renyi graphs become computationally intractable below the `Kesten-Stigum threshold' $d_{KS,k} = (k-1)^2$. Along the way, we use the celebrated Ihara-Bass identity and a carefully constructed non-backtracking random walk to prove two deterministic results of independent interest: a lower bound on the vector chromatic number (and thus the chromatic number) using the spectrum of the non-backtracking walk matrix, and an upper bound dependent only on the girth and universal cover. Our upper bound may be equivalently viewed as a generalization of the Alon-Boppana theorem to irregular graphs

Includes members:
  Member "an alon boppana type bound for weighted graphs and lowerbounds for spectral sparsification":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "deterministic and randomized actuator scheduling with guaranteed performance bounds")
  Member "how well do local algorithms solve semidefinite programs":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "the power of sum of squares for detecting hidden structures")
  Member "spectral redemption in clustering sparse networks":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "approximating spectral clustering via sampling a review")
  Member "community detection thresholds and the weak ramanujan property":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "from tree matching to sparse graph alignment")
  Member "approximate graph coloring by semidefinite programming":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "positive semidefinite programming mixed parallel and width independent")

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)