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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 X i + Y j . The algorithm relies on layer-ordered heaps, partial orderings of exponentially sized layers. The algorithm relies only on median-of-medians and is simple to implement. Furthermore, it uses data structures contiguous in memory, cache efficient, and fast in practice. The presented algorithm is demonstrated to be theoretically optimal.Deep neural networks have been