# Sparse nonnegative convolution is equivalent to dense nonnegative convolution

@article{Bringmann2021SparseNC,
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},
year={2021}
}
• Published 12 May 2021
• Computer Science
• 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…
4 Citations

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### Deterministic and Las Vegas Algorithms for Sparse Nonnegative Convolution

• Computer Science
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• 2022
This paper presents the first deterministic near-linear-time algorithm for computing sparse nonnegative convolutions, which immediately gives improved deterministic algorithms for the state-of-the-art of output-sensitive Subset Sum, block-mass pattern matching, N -fold Boolean convolution, and others, matching up to log-factors the fastest known randomized algorithms for these problems.

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