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Optimally selecting the top k values from X + Y with layer-ordered heaps
1Department of Computer Science, University of Montana, Missoula, Montana, United States.
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 . 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.
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