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 "almost polynomial ratio eth hardness of approximating densest k subgraph"):
  Abstract: In the Densest $k$-Subgraph problem, given an undirected graph $G$ and an integer $k$, the goal is to find a subgraph of $G$ on $k$ vertices that contains maximum number of edges. Even though the state-of-the-art algorithm for the problem achieves only $O(n^{1/4 + \varepsilon})$ approximation ratio (Bhaskara et al., 2010), previous attempts at proving hardness of approximation, including those under average case assumptions, fail to achieve a polynomial ratio; the best ratios ruled out under any worst case assumption and any average case assumption are only any constant (Raghavendra and Steurer, 2010) and $2^{\Omega(\log^{2/3} n)}$ (Alon et al., 2011) respectively. #R##N#In this work, we show, assuming the exponential time hypothesis (ETH), that there is no polynomial-time algorithm that approximates Densest $k$-Subgraph to within $n^{1/(\log \log n)^c}$ factor of the optimum, where $c > 0$ is a universal constant independent of $n$. In addition, our result has "perfect completeness", meaning that we prove that it is ETH-hard to even distinguish between the case in which $G$ contains a $k$-clique and the case in which every induced $k$-subgraph of $G$ has density at most $1/n^{-1/(\log \log n)^c}$ in polynomial time. #R##N#Moreover, if we make a stronger assumption that there is some constant $\varepsilon > 0$ such that no subexponential-time algorithm can distinguish between a satisfiable 3SAT formula and one which is only $(1 - \varepsilon)$-satisfiable (also known as Gap-ETH), then the ratio above can be improved to $n^{f(n)}$ for any function $f$ whose limit is zero as $n$ goes to infinity (i.e. $f \in o(1)$).

Includes members:
  Member "settling the complexity of computing approximate two player nash equilibria":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "complexity theory game theory and economics the barbados lectures")
  Member "inapproximability results for approximate nash equilibria":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "public bayesian persuasion being almost optimal and almost persuasive")
  Member "a birthday repetition theorem and complexity of approximating dense csps":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "parameterized inapproximability for steiner orientation by gap amplification")
  Member "partitioning a graph into small pieces with applications to path transversal":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "parameterized complexity of safe set")
  Member "combining traditional marketing and viral marketing with amphibious influence maximization":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "maximizing welfare in social networks under a utility driven influence diffusion model")
  Member "eth hardness for densest k subgraph with perfect completeness":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "complexity theory game theory and economics the barbados lectures")
  Member "eth hardness for signaling in symmetric zero sum games":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "inapproximability of vc dimension and littlestone s dimension")
  Member "approximating dense max 2 csps":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "amplification and derandomization without slowdown")

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)