# Questions tagged [convolution]

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### Subquadratic 3SUM when one set is in [n^1.99]

Chan and Lewenstein (STOC 2015) said: 3SUM for three integer sets where only one set is assumed to be in $[n^{2−\delta}]$ can still be solved in subquadratic time (by doing several FFTs, without ...
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### Is gaussian smoothing possible in less operations than O(N log N)

Gaussian filtering is popular in applications, for my question it can be written as (I've fixed the size of window): $$y_i = \sum_{j = 1}^{n} x_j e^{(i - j)^2}, \qquad i = 1, 2, ..., n$$ One can ...
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### Finding witness in minkowski sum of integers

Let $A$ and $B$ be subsets of $\{0,\ldots,n\}$. We are interested in finding the Minkowski sum $A+B=\{a+b~|~a\in A,b\in B\}$. $\chi_X:\{0,\ldots,2n\}\to \{0,1\}$ is a characteristic function of $X$ ...
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### Algorithm for multiplying multivariate polynomials in a commutative ring

Let $R$ be a commutative ring. Let $f(x_1, \dots, x_n), g(x_1, \dots, x_n)$ be two multivariate polynomials with the same $x_i$-terms with maximal total degree $\delta$, but with different ...
We can do convolution in $O(n\log n)$ for plus/multiply polynomials with FFT. However, the approach doesn't seem very generalisable to rings in general. Has there been any progress over the naive \$O(...