In light of the recent pandemic and the shortage of vaccinations during their roll-out, questions arose regarding the best strategy to achieve immunity throughout the population by adjusting the time gap between the two necessary vaccination doses. This strategy has already been studied from different angles by various researches. However, the deliveries of vaccination doses also proved to be highly uncertain, with manufacturers not being able to deliver the promised amount of vaccines on time.
In this paper, we study the robust version of this problem and its generalization to matchings on arbitrary graphs. By exploring the problem, we show that it is weakly NP-hard for a constant number of scenarios and strongly NP-hard else. Further, we propose a pseudo-polynomial algorithm for the weakly NP-hard subproblem with a constant number of scenarios and time between both doses. Finally, we perform computational experiments to better understand the behavior of the problem.
Citation
Jenny Segschneider, Arie M.C.A. Koster. (2024). Robust two-dose vaccination schemes and the directed b-matching problem. Discrete Applied Mathematics, Volume 356, 369-392. https://doi.org/10.1016/j.dam.2024.06.029