Let $k \geq 2$ be a constant. Given any $k$ convex polygons in the plane with a total of $n$ vertices, we present an $O(n\log^{2k-3}n)$ time algorithm that finds a translation of each of the polygons such that the area of intersection of the $k$ polygons is maximized. Given one such placement, we also give an $O(n)$ time algorithm which computes the set of all translations of the polygons which achieve this maximum.

翻译：设 $k \geq 2$ 为常数。给定平面上总顶点数为 $n$ 的任意 $k$ 个凸多边形，我们提出一种时间复杂度为 $O(n\log^{2k-3}n)$ 的算法，该算法可找到每个多边形的一个平移，使得这 $k$ 个多边形的交集面积最大化。给定这样一个放置方案后，我们还给出一种 $O(n)$ 时间算法，用于计算所有能使该交集面积达到最大值的多边形平移集合。