# Optimal selection on X+Y simplified with layer-ordered heaps

Selection on the Cartesian sum, A+B, is a classic and important problem. Frederickson's 1993 algorithm produced the first algorithm that made possible an optimal runtime. Kaplan et al.'s recent 2018 paper descibed an alternative optimal algorithm by using Chazelle's soft heaps. These extant optimal algorithms are very complex; this complexity can lead to difficulty implementing them and to poor performance in practice. Here, a new optimal algorithm is presented, which uses layer-ordered heaps. This new algorithm is both simple to implement and practically efficient.

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