2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/168585For the \textsc{Minkowski Sum Selection} problem with linear objective functions, we obtain the following results: (1) optimal $O(n\log n)$ time algorithms for $λ=1$; (2) $O(n\log^2 n)$ time deterministic algorithms and expected $O(n\log n)$ time randomized algorithms for any fixed $λ>1$. For the \textsc{Minkowski Sum Finding} problem with linear objective functions or objective functions of the form $f(x,y)=\frac{by}{ax}$, we construct optimal $O(n\log n)$ time algorithms for any fixed $λ\geq 1$.23 pages, 10 figures, accepted by ISAAC 2008Data Structures and AlgorithmsComputational Geometrytext