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 "hardness amplification of optimization problems"):
  Abstract: In this paper, we prove a general hardness amplification scheme for optimization problems based on the technique of direct products. We say that an optimization problem $\Pi$ is direct product feasible if it is possible to efficiently aggregate any $k$ instances of $\Pi$ and form one large instance of $\Pi$ such that given an optimal feasible solution to the larger instance, we can efficiently find optimal feasible solutions to all the $k$ smaller instances. Given a direct product feasible optimization problem $\Pi$, our hardness amplification theorem may be informally stated as follows: If there is a distribution $\mathcal{D}$ over instances of $\Pi$ of size $n$ such that every randomized algorithm running in time $t(n)$ fails to solve $\Pi$ on $\frac{1}{\alpha(n)}$ fraction of inputs sampled from $\mathcal{D}$, then, assuming some relationships on $\alpha(n)$ and $t(n)$, there is a distribution $\mathcal{D}'$ over instances of $\Pi$ of size $O(n\cdot \alpha(n))$ such that every randomized algorithm running in time $\frac{t(n)}{poly(\alpha(n))}$ fails to solve $\Pi$ on $\frac{99}{100}$ fraction of inputs sampled from $\mathcal{D}'$. As a consequence of the above theorem, we show hardness amplification of problems in various classes such as NP-hard problems like Max-Clique, Knapsack, and Max-SAT, problems in P such as Longest Common Subsequence, Edit Distance, Matrix Multiplication, and even problems in TFNP such as Factoring and computing Nash equilibrium.

Includes members:
  Member "on nondeterministic derandomization of freivalds algorithm consequences avenues and algorithmic progress":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "new algorithms and lower bounds for all pairs max flow in undirected graphs")
  Member "integer factoring and modular square roots":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "the classes ppa k existence from arguments modulo k")
  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 "simulating branching programs with edit distance and friends or a polylog shaved is a lower bound made":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "streaming with oracle new streaming algorithms for edit distance and lcs")
  Member "why walking the dog takes time frechet distance has no strongly subquadratic algorithms unless seth fails":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "graphs cannot be indexed in polynomial time for sub quadratic time string matching unless seth fails")
  Member "inapproximability of nash equilibrium":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "the complexity of interactively learning a stable matching by trial and error")
  Member "edit distance cannot be computed in strongly subquadratic time unless seth is false":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "streaming with oracle new streaming algorithms for edit distance and lcs")
  Member "settling the complexity of computing two player nash equilibria":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "learning zero sum simultaneous move markov games using function approximation and correlated equilibrium")

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)