Let $P$ be a set of $n$ points in $\mathbb{R}^2$. For a given positive integer $w<n$, our objective is to find a set $C \subset P$ of points, such that $CH(P\setminus C)$ has the smallest number of vertices and $C$ has at most $n-w$ points. We discuss the $O(wn^3)$ time dynamic programming algorithm for monotone decomposable functions (MDF) introduced for finding a class of optimal convex $w$-gons, with vertices chosen from $P$, and improve it to $O(n^3 \log w)$ time, which gives an improvement to the existing algorithm for MDFs if their input is a convex polygon.

翻译：让 $P 成为 $mathbb{R ⁇ 2$ 的一组零点。 对于给定正整数 $w <n$, 我们的目标是找到一套 $C\ subset P$ 的点数, 这样, $CH( P\ setminus C) 的顶点数最小, $C 的点数最多为 $n- w$ 。 我们讨论 $O( wn) 3) $ 用于单体分解函数的时间动态编程算法( MDF ), 以寻找一个从 $P 中选择的顶级convex $w$-gon, 并把它改进为 $O( n ⁇ 3\ log w) 的时间, 如果 MDF 输入为 矩形, 则可以改进 MDF 的现有算法 。