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 "tighter fourier transform complexity tradeoffs"):
  Abstract: The Fourier Transform is one of the most important linear transformations used in science and engineering. Cooley and Tukey's Fast Fourier Transform (FFT) from 1964 is a method for computing this transformation in time $O(n\log n)$. Achieving a matching lower bound in a reasonable computational model is one of the most important open problems in theoretical computer science. #R##N#In 2014, improving on his previous work, Ailon showed that if an algorithm speeds up the FFT by a factor of $b=b(n)\geq 1$, then it must rely on computing, as an intermediate "bottleneck" step, a linear mapping of the input with condition number $\Omega(b(n))$. Our main result shows that a factor $b$ speedup implies existence of not just one but $\Omega(n)$ $b$-ill conditioned bottlenecks occurring at $\Omega(n)$ different steps, each causing information from independent (orthogonal) components of the input to either overflow or underflow. This provides further evidence that beating FFT is hard. Our result also gives the first quantitative tradeoff between computation speed and information loss in Fourier computation on fixed word size architectures. The main technical result is an entropy analysis of the Fourier transform under transformations of low trace, which is interesting in its own right.

Includes members:
  Member "an n log n lower bound for fourier transform computation in the well conditioned model":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "paraunitary matrices entropy algebraic condition number and fourier computation")
  Member "a lower bound for fourier transform computation in a linear model over 2x2 unitary gates using matrix entropy":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "the complexity of computing almost unitary matrices with eps copies of the fourier transform")
  Member "new and improved johnson lindenstrauss embeddings via the restricted isometry property":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "finding the mode of a kernel density estimate")

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)