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 "the complexity of computing a fourier perturbation"):
  Abstract: The complexity of computing the Fourier transform is a longstanding open problem. Very recently, Ailon (2013, 2014, 2015) showed in a collection of papers that, roughly speaking, a speedup of the Fourier transform computation implies numerical ill-condition. The papers also quantify this tradeoff. The main method for proving these results is via a potential function called quasi-entropy, reminiscent of Shannon entropy. The quasi-entropy method opens new doors to understanding the computational complexity of the important Fourier transformation. However, it suffers from various drawbacks. This paper, motivated by one such drawback, eliminates it by extending the method. The argument goes as follows: If instead of computing the Fourier transform Fx of input x ∈ Rn we were to compute a Fourier e-perturbation, defined as (Id+eF )x, then the quasientropy method in the well-conditioned regime would, without any adjustments, lead to a linear algebraic lower bound of Ω(en logn) many operations (counting additions and multiplications on scalar variables). Had this bound been matched by an algorithm, then we would have been able to extract Fx in time O(en logn) by first computing (Id+eF )x, then subtracting x from the output and dividing the result by e. By taking e = Θ(1/ √ logn) we could artificially drive the computation time toward the trivial linear time lower bound. Such a scheme would suffer on a real computer from numerical errors, but this could be avoided by extending the computer word size by only Θ(log e) = Θ(log log n) bits. The end result is a Fourier algorithm in running time O(n log logn) (counting logical bit operations, and using fast integer multiplication). We generalize the quasi-entropy method so as to show that driving e down does not allow such a free ride in case of the Walsh-Hadamard Fourier transform, and that the linear algebraic lower bound is, in fact, Ω((n logn)/ log e). This exactly ‘cancels out’ the numerical accuracy overhead. It also strengthens our belief that, roughly speaking, Fourier computation requires Ω(n logn) time in a computational model that takes into account numerical accuracy and logical bit operations. ∗ nailon@cs.technion.ac.il gal2016@gmail.com

Includes members:
  Member "even faster integer multiplication":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "on the i o complexity of hybrid algorithms for integer multiplication")
  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 "improved matrix algorithms via the subsampled randomized hadamard transform":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "improved subsampled randomized hadamard transform for linear svm")

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)