Pairwise distance with respect to 2 columns of the second matrix

[biona001]

I am interested in a funny scenario where given matrices X and Y, I want to compute

euclidean(x, yi, yj) = ||x - yi - yj||^2

for all columns of X and all column pairs of Y. I am wondering if there's some way to use this package for this purpose?

[biona001]

More specifically, I am only interested in the pairs (i, j) such that this distance is minimized for every column of x. If we compute the distance for all such pairs then the distance matrix may be too large as Y increases.