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 "the average case complexity of counting cliques in erdos renyi hypergraphs"):
  Abstract: The complexity of clique problems on Erdos-Renyi random graphs has become a central topic in average-case complexity. Algorithmic phase transitions in these problems have been shown to have broad connections ranging from mixing of Markov chains to information-computation gaps in high-dimensional statistics. We consider the problem of counting $k$-cliques in $s$-uniform Erdos-Renyi hypergraphs $G(n, c, s)$ with edge density $c$, and show that its fine-grained average-case complexity can be based on its worst-case complexity. We prove the following: #R##N#1. Dense Erdos-Renyi hypergraphs: Counting $k$-cliques on $G(n, c, s)$ with $k$ and $c$ constant matches its worst-case complexity up to a $\mathrm{polylog}(n)$ factor. Assuming ETH, it takes $n^{\Omega(k)}$ time to count $k$-cliques in $G(n, c, s)$ if $k$ and $c$ are constant. #R##N#2. Sparse Erdos-Renyi hypergraphs: When $c = \Theta(n^{-\alpha})$, our reduction yields different average-case phase diagrams depicting a tradeoff between runtime and $k$ for each fixed $\alpha$. Assuming the best-known worst-case algorithms are optimal, in the graph case of $s = 2$, we establish that the exponent in $n$ of the optimal running time for $k$-clique counting in $G(n, c, s)$ is $\frac{\omega k}{3} - C \alpha \binom{k}{2} + O_{k, \alpha}(1)$, where $\frac{\omega}{9} \le C \le 1$ and $\omega$ is the matrix multiplication constant. In the hypergraph case of $s \ge 3$, we show a lower bound at the exponent of $k - \alpha \binom{k}{s} + O_{k, \alpha}(1)$ which surprisingly is tight exactly for the set of $c$ above the Erdos-Renyi $k$-clique percolation threshold. #R##N#Our reduction yields the first known average-case hardness result on Erdos-Renyi hypergraphs based on worst-case hardness conjectures. We also analyze several natural algorithms for counting $k$-cliques in $G(n, c, s)$ that establish our upper bounds in the sparse case $c = \Theta(n^{-\alpha})$.

Includes members:
  Member "optimal average case reductions to sparse pca from weak assumptions to strong hardness":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "adversarially robust low dimensional representations")
  Member "reducibility and computational lower bounds for problems with planted sparse structure":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "adversarially robust low dimensional representations")
  Member "a nearly tight sum of squares lower bound for the planted clique problem":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "broadcast congested clique planted cliques and pseudorandom generators")
  Member "on independent sets in random graphs":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "online learning with feedback graphs and switching costs")
  Member "incoherence optimal matrix completion":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "matrix completion with prior subspace information via maximizing correlation")
  Member "hidden cliques and the certification of the restricted isometry property":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "on the restricted isometry of the columnwise khatri rao product")
  Member "nuclear norm minimization for the planted clique and biclique problems":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "average case lower bounds for learning sparse mixtures robust estimation and semirandom adversaries")

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)