Optimal selection on $X+Y$ simplified with layer-ordered heaps
Oliver Serang · arXiv (Cornell University) · 2020
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 \emph{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.