  The layer-ordered heap (LOH) is a simple, recently proposed data structure
used in optimal selection on $X+Y$, thealgorithm with the best known runtime
for selection on $X_1+X_2+\cdots+X_m$, and the fastest method in practice for
computing the most abundant isotope peaks in a chemical compound. Here, we
introduce a few algorithms for constructing LOHs, analyze their complexity, and
demonstrate that one algorithm is optimal for building a LOH of any rank
$\alpha$. These results are shown to correspond with empirical experiments of
runtimes when applying the LOH construction algorithms to a common task in
machine learning.
