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: "a birthday repetition theorem and complexity of approximating dense csps"
  Abstract: A $(k \times l)$-birthday repetition $\mathcal{G}^{k \times l}$ of a two-prover game $\mathcal{G}$ is a game in which the two provers are sent random sets of questions from $\mathcal{G}$ of sizes $k$ and $l$ respectively. These two sets are sampled independently uniformly among all sets of questions of those particular sizes. We prove the following birthday repetition theorem: when $\mathcal{G}$ satisfies some mild conditions, $val(\mathcal{G}^{k \times l})$ decreases exponentially in $\Omega(kl/n)$ where $n$ is the total number of questions. Our result positively resolves an open question posted by Aaronson, Impagliazzo and Moshkovitz (CCC 2014). #R##N#As an application of our birthday repetition theorem, we obtain new fine-grained hardness of approximation results for dense CSPs. Specifically, we establish a tight trade-off between running time and approximation ratio for dense CSPs by showing conditional lower bounds, integrality gaps and approximation algorithms. In particular, for any sufficiently large $i$ and for every $k \geq 2$, we show the following results: #R##N#- We exhibit an $O(q^{1/i})$-approximation algorithm for dense Max $k$-CSPs with alphabet size $q$ via $O_k(i)$-level of Sherali-Adams relaxation. #R##N#- Through our birthday repetition theorem, we obtain an integrality gap of $q^{1/i}$ for $\tilde\Omega_k(i)$-level Lasserre relaxation for fully-dense Max $k$-CSP. #R##N#- Assuming that there is a constant $\epsilon > 0$ such that Max 3SAT cannot be approximated to within $(1-\epsilon)$ of the optimal in sub-exponential time, our birthday repetition theorem implies that any algorithm that approximates fully-dense Max $k$-CSP to within a $q^{1/i}$ factor takes $(nq)^{\tilde \Omega_k(i)}$ time, almost tightly matching the algorithmic result based on Sherali-Adams relaxation.

Connected through hyperedge HE-1 (induced by source paper "parameterized inapproximability for steiner orientation by gap amplification"):
  with members:
    - "tight fpt approximations for k median and k means"
    - "constant factor fpt approximation for capacitated k median"
    - "faster exact and approximate algorithms for k cut"
    - "from gap eth to fpt inapproximability clique dominating set and more"
    - "completely inapproximable monotone and antimonotone parameterized problems"
    - "almost polynomial ratio eth hardness of approximating densest k subgraph"
    - "directed multicut is w 1 hard even for four terminal pairs"
    - "the parameterized complexity of k biclique"

Connected through hyperedge HE-2 (induced by source paper "tight running time lower bounds for strong inapproximability of maximum k coverage unique set cover and related problems via t wise agreement testing theorem"):
  with members:
    - "a simple gap producing reduction for the parameterized set cover problem"
    - "parameterized intractability of even set and shortest vector problem"
    - "parameterized inapproximability of exact cover and nearest codeword"
    - "tight fpt approximations for k median and k means"
    - "agreement testing theorems on layered set systems"
    - "towards a general direct product testing theorem"
    - "gap s eth hardness of svp"
    - "eth hardness of approximating 2 csps and directed steiner network"

Connected through hyperedge HE-3 (induced by source paper "approximating constraint satisfaction problems on high dimensional expanders"):
  with members:
    - "agreement testing theorems on layered set systems"
    - "good distance lattices from high dimensional expanders"
    - "log concave polynomials ii high dimensional walks and an fpras for counting bases of a matroid"
    - "sum of squares lower bounds for refuting any csp"
    - "high dimensional random walks and colorful expansion"
    - "a new regularity lemma and faster approximation algorithms for low threshold rank graphs"
    - "faster sdp hierarchy solvers for local rounding algorithms"
    - "rounding semidefinite programming hierarchies via global correlation"

Connected through hyperedge HE-4 (induced by source paper "parameterized intractability of even set and shortest vector problem"):
  with members:
    - "gap s eth hardness of svp"
    - "parameterized complexity of csp for infinite constraint languages"
    - "on the quantitative hardness of cvp"
    - "on the hardness of learning sparse parities"
    - "tensor based hardness of the shortest vector problem to within almost polynomial factors"
    - "a simple deterministic reduction for the gap minimum distance of code problem"
    - "new lattice based cryptographic constructions"

Connected through hyperedge HE-5 (induced by source paper "approximation and hardness of shift bribery"):
  with members:
    - "from gap eth to fpt inapproximability clique dominating set and more"
    - "almost polynomial ratio eth hardness of approximating densest k subgraph"
    - "prices matter for the parameterized complexity of shift bribery"
    - "campaign management under approval driven voting rules"
    - "the constant inapproximability of the parameterized dominating set problem"
    - "the complexity of probabilistic lobbying"
    - "how hard is bribery in elections"

Connected through hyperedge HE-6 (induced by source paper "hardness amplification of optimization problems"):
  with members:
    - "on nondeterministic derandomization of freivalds algorithm consequences avenues and algorithmic progress"
    - "integer factoring and modular square roots"
    - "simulating branching programs with edit distance and friends or a polylog shaved is a lower bound made"
    - "why walking the dog takes time frechet distance has no strongly subquadratic algorithms unless seth fails"
    - "inapproximability of nash equilibrium"
    - "edit distance cannot be computed in strongly subquadratic time unless seth is false"
    - "settling the complexity of computing two player nash equilibria"

Connected through hyperedge HE-7 (induced by source paper "treewidth pliability and ptas for max csps"):
  with members:
    - "eth hardness of approximating 2 csps and directed steiner network"
    - "thin graph classes and polynomial time approximation schemes"
    - "from gap eth to fpt inapproximability clique dominating set and more"
    - "the complexity of general valued csps seen from the other side"

Connected through hyperedge HE-8 (induced by source paper "imperfect gaps in gap eth and pcps"):
  with members:
    - "gap s eth hardness of svp"
    - "from gap eth to fpt inapproximability clique dominating set and more"

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)