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: "inapproximability of np complete variants of nash equilibrium"
  Abstract: In recent work of Hazan and Krauthgamer (SICOMP 2011), it was shown that finding an $\eps$-approximate Nash equilibrium with near-optimal value in a two-player game is as hard as finding a hidden clique of size $O(\log n)$ in the random graph $G(n,1/2)$. This raises the question of whether a similar intractability holds for approximate Nash equilibrium without such constraints. We give evidence that the constraint of near-optimal value makes the problem distinctly harder: a simple algorithm finds an optimal 1/2-approximate equilibrium, while finding strictly better than 1/2-approximate equilibria is as hard as the Hidden Clique problem. This is in contrast to the unconstrained problem where more sophisticated algorithms, achieving better approximations, are known. #R##N#Unlike general Nash equilibrium, which is in PPAD, optimal (maximum value) Nash equilibrium is NP-hard. We proceed to show that optimal Nash equilibrium is just one of several known NP-hard problems related to Nash equilibrium, all of which have approximate variants which are as hard as finding a planted clique. In particular, we show this for approximate variants of the following problems: finding a Nash equilibrium with value greater than $\eta$ (for any $\eta>0$, even when the best Nash equilibrium has value $1-\eta$), finding a second Nash equilibrium, and finding a Nash equilibrium with small support. #R##N#Finally, we consider the complexity of approximate pure Bayes Nash equilibria in two-player games. Here we show that for general Bayesian games the problem is NP-hard. For the special case where the distribution over types is uniform, we give a quasi-polynomial time algorithm matched by a hardness result based on the Hidden Clique problem.

Connected through hyperedge HE-1 (induced by source paper "reducibility and computational lower bounds for problems with planted sparse structure"):
  with members:
    - "sherali adams integrality gaps matching the log density threshold"
    - "on finding dense common subgraphs"
    - "robust sparse estimation tasks in high dimensions"
    - "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"
    - "feeling the bern adaptive estimators for bernoulli probabilities of pairwise comparisons"
    - "statistical query lower bounds for robust estimation of high dimensional gaussians and gaussian mixtures"

Connected through hyperedge HE-2 (induced by source paper "approximating the existential theory of the reals"):
  with members:
    - "computing constrained approximate equilibria in polymatrix games"
    - "approximating nash equilibria in tree polymatrix games"
    - "lipschitz continuity and approximate equilibria"
    - "empirical distribution of equilibrium play and its testing application"
    - "most tensor problems are np hard"

Connected through hyperedge HE-3 (induced by source paper "computing constrained approximate equilibria in polymatrix games"):
  with members:
    - "distributed methods for computing approximate equilibria"
    - "fptas for mixed strategy nash equilibria in tree graphical games and their generalizations"
    - "approximating nash equilibria in tree polymatrix games"
    - "an empirical study on computing equilibria in polymatrix games"
    - "inapproximability results for approximate nash equilibria"
    - "finding any nontrivial coarse correlated equilibrium is hard"
    - "inapproximability of nash equilibrium"
    - "computing approximate nash equilibria in polymatrix games"

Connected through hyperedge HE-4 (induced by source paper "settling the complexity of computing approximate two player nash equilibria"):
  with members:
    - "almost polynomial ratio eth hardness of approximating densest k subgraph"
    - "detecting communities is hard and counting them is even harder"
    - "approximating nash equilibria in tree polymatrix games"
    - "the query complexity of correlated equilibria"
    - "communication complexity of approximate nash equilibria"
    - "inapproximability results for approximate nash equilibria"
    - "well supported versus approximate nash equilibria query complexity of large games"
    - "near optimal hardness results for signaling in bayesian games"

Connected through hyperedge HE-5 (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"
    - "sum of squares lower bounds for planted clique"
    - "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"

Connected through hyperedge HE-6 (induced by source paper "inapproximability results for approximate nash equilibria"):
  with members:
    - "distributed methods for computing approximate equilibria"
    - "settling the complexity of computing approximate two player nash equilibria"
    - "am with multiple merlins"
    - "approximate well supported nash equilibria below two thirds"

Connected through hyperedge HE-7 (induced by source paper "computing approximate nash equilibria in polymatrix games"):
  with members:
    - "an empirical study of finding approximate equilibria in bimatrix games"
    - "inapproximability of nash equilibrium"
    - "approximate well supported nash equilibria in symmetric bimatrix games"
    - "approximate well supported nash equilibria below two thirds"
    - "the complexity of non monotone markets"
    - "a direct reduction from k player to 2 player approximate nash equilibrium"
    - "approximate equilibria in games with few players"
    - "settling the complexity of computing two player nash equilibria"

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)