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