We study a natural extension to the well-known convex hull problem by introducing multiplicity: if we are given a set of convex polygons, and we are allowed to partition the set into multiple components and take the convex hull of each individual component, what is the minimum total sum of the perimeters of the convex hulls? We show why this problem is intriguing, and then introduce a novel algorithm with a run-time cubic in the total number of vertices. In the case that the input polygons are disjoint, we show an optimization that achieves a run-time that, in most cases, is cubic in the total number of polygons, within a logarithmic factor.
翻译：我们通过引入多重性来研究众所周知的锥形船体问题的自然延伸:如果我们得到一套锥形多边形,并且我们被允许将组装分成多个组成部分,并采取每个组成部分的锥形船体,那么锥形船体周围的最小总和是多少?我们说明为什么这个问题令人感兴趣,然后在脊椎的总数中引入一种带有运行时立立方的新型算法。如果输入多边形是脱节的,我们则展示一种优化,实现运行时间,在多数情况下,在逻辑系数范围内,在多边形的总数中是立方的。
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