Minkowski Sum Selection and Finding
  For the \textsc{Minkowski Sum Selection} problem with linear objective functions, we obtain the following results: (1) optimal $O(n\log n)$ time algorithms for $\lambda=1$; (2) $O(n\log^2 n)$ time deterministic algorithms and expected $O(n\log n)$ time randomized algorithms for any fixed $\lambda>1$. 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 $\lambda\geq 1$. 
Cheng-Wei Luo, Hsiao-Fei Liu, Peng-An Chen, and Kun-Mao Chao