Selection and sorting the Cartesian sum, X+Y, are classic and important problems. Here, a new algorithm is presented, which generates the top k values of the form Xi+Yj. The algorithm relies only on median-of-medians and is simple to implement. Furthermore, it uses data structures contiguous in memory, and is fast in practice. The presented algorithm is demonstrated to be theoretically optimal.
@article{arxiv.2001.11607,
title = {Optimally selecting the top $k$ values from $X+Y$ with layer-ordered heaps},
author = {Oliver Serang},
journal= {arXiv preprint arXiv:2001.11607},
year = {2020}
}