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.
We introduce the maximum n-times coverage problem that selects k overlays to maximize the summed coverage of weighted elements, where each element must be covered at least n times . 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. Maximum n-times coverage is a generalization of the multi-set multi-cover problem, is NP-complete, and is not submodular. We introduce two new practical solutions for n-times coverage based on integer linear programming and sequential greedy optimization. We show that maximum n-times coverage is a natural way to frame peptide vaccine design, and find that it produces a pan-strain COVID-19 vaccine design that is superior to 29 other published designs in predicted population coverage and the expected number of peptides displayed by each individual's HLA molecules.
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COVID-19 peptide vaccine