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Selection and sorting the Cartesian sum, $X+Y$, are classic and importantproblems. Here, a new algorithm is presented, which generates the top $k$values of the form $X_i+Y_j$. The algorithm relies only on median-of-mediansand is simple to implement. Furthermore, it uses data structures contiguous inmemory, and is fast in practice. The presented algorithm is demonstrated to betheoretically optimal.

Optimally selecting the top $k$ values from $X+Y$ with layer-ordered heaps