# Optimal construction of a layer-ordered heap

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+⋯+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 α. These results are shown to correspond with empirical experiments of runtimes when applying the LOH construction algorithms to a common task in machine learning.

READ FULL TEXT