Maximum n-times Coverage for COVID-19 Vaccine Design

In the maximum $n$-times coverage problem, we are provided a set of elements, a weight for each element, and a set of overlays where each overlay specifies an element specific coverage of zero or more times. The goal is to select up to $k$ overlays such that the sum of the weights of elements that are covered at least $n$ times is maximized. We also define the min-cost $n$-times coverage problem where the objective is to select the minimum set of overlays such that the sum of the weights of elements that are covered at least $n$ times is at least $\tau$. We show that the $n$-times coverage objective is not submodular, and we present an efficient solution by sequential greedy optimization. We frame the design of a peptide vaccine for COVID-19 as maximum $n$-times coverage using machine learning defined candidate peptide sets, and show that our solution is superior to 29 other published COVID-19 peptide vaccine designs in predicted population coverage and the expected number of peptides displayed by each individual's HLA molecules.