Sparse nonnegative convolution is equivalent to dense nonnegative convolution

  title={Sparse nonnegative convolution is equivalent to dense nonnegative convolution},
  author={Karl Bringmann and Nick Fischer and Vasileios Nakos},
  journal={Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing},
Computing the convolution A ⋆ B of two length-n vectors A,B is an ubiquitous computational primitive, with applications in a variety of disciplines. Within theoretical computer science, applications range from string problems to Knapsack-type problems, and from 3SUM to All-Pairs Shortest Paths. These applications often come in the form of nonnegative convolution, where the entries of A,B are nonnegative integers. The classical algorithm to compute A⋆ B uses the Fast Fourier Transform (FFT) and… 

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