Fast exact computation of the $k$ most abundant isotope peaks with layer-ordered heaps

The theoretical computation of isotopic distribution of compounds is crucial in many important applications of mass spectrometry, especially as machine precision grows. A considerable amount of good tools have been created in the last decade for doing so. In this paper we present a novel algorithm for calculating the top $k$ peaks of a given compound. The algorithm takes advantage of layer-ordered heaps used in an optimal method of selection on $X+Y$ and is able to efficiently calculate the top $k$ peaks on very large molecules. Among its peers, this algorithm shows a significant speedup on molecules whose elements have many isotopes. The algorithm obtains a speedup of more than 31x when compared to $\textsc{IsoSpec}$ on \ch{Au2Ca10Ga10Pd76} when computing 47409787 peaks, which covers 0.999 of the total abundance.