Given a rectangle $R$ with area $A$ and a set of areas $L=\{A_1,...,A_n\}$ with $\sum_{i=1}^n A_i = A$, we consider the problem of partitioning $R$ into $n$ sub-regions $R_1,...,R_n$ with areas $A_1,...,A_n$ in a way that the total perimeter of all sub-regions is minimized. The goal is to create square-like sub-regions, which are often more desired. We propose a divide and conquer algorithm for this problem that finds factor $1.2$--approximate solutions in $\mathcal{O}(n\log n)$ time.

翻译：给定一个面积为 $A$ 的矩形 $R$ 以及一组面积 $L=\{A_1,...,A_n\}$，满足 $\sum_{i=1}^n A_i = A$。我们考虑将 $R$ 划分为 $n$ 个子区域 $R_1,...,R_n$，其面积分别为 $A_1,...,A_n$，并使得所有子区域的总周长最小化的问题。目标是创建更受青睐的类正方形子区域。我们针对该问题提出一种分治算法，能在 $\mathcal{O}(n\log n)$ 时间内求得因子为 $1.2$ 的近似解。