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 "paraunitary matrices entropy algebraic condition number and fourier computation"):
  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 $O(n\log n)$. From a lower bound perspective, relatively little is known. Ailon shows in 2013 an $\Omega(n\log n)$ bound for computing the normalized Fourier Transform assuming only unitary operations on two coordinates are allowed at each step, and no extra memory is allowed. In 2014, Ailon then improved the result to show that, in a $\kappa$-well conditioned computation, Fourier computation can be sped up by no more than $O(\kappa)$. The main conjecture is that Ailon's result can be exponentially improved, in the sense that $\kappa$-well condition cannot admit $\omega(\log \kappa)$ speedup. #R##N#The main result here is that `algebraic' $\kappa$-well condition admits no more than $O(\sqrt \kappa)$ speedup. The definition of algebraic condition number is obtained by formally viewing multiplication by constants, as performed by the algorithm, as multiplication by indeterminates, giving rise to computation over polynomials. The algebraic condition number is related to the degree of these polynomials. Using the maximum modulus theorem from complex analysis, we show that algebraic condition number upper bounds standard condition number, and equals it in certain cases. Algebraic condition number is an interesting measure of numerical computation stability in its own right. Moreover, we believe that the approach of algebraic condition number has a good chance of establishing an algebraic version of the main conjecture.

Includes members:
  Member "the complexity of computing a fourier perturbation":
    also connected through other hyperedges:
      (none)
  Member "the johnson lindenstrauss lemma is optimal for linear dimensionality reduction":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "sub gaussian matrices on sets optimal tail dependence and applications")
  Member "an n log n lower bound for fourier transform computation in the well conditioned model":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "tighter fourier transform complexity tradeoffs")
  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-3 (induced by source paper "the complexity of computing almost unitary matrices with eps copies of the fourier transform")

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)