4/3矩形平铺下限
4/3 Rectangle Tiling lower bound
摘要：
我们考虑的问题如下：给定一个正数的$n \times n$数组$A$，找到一个最多使用$p$矩形的平铺（这意味着每个数组元素必须被某个矩形覆盖，并且没有两个矩形必须重叠），使任何矩形的最大权重最小化（矩形的权重是它所覆盖的元素的总和）。我们证明了，这是NP-困难的近似这个问题的一个因素内的\textbf{1$\frac{1}{3}$}（以前的最佳结果是$1\frac{1}{4}$）。
英文摘要：
The problem that we consider is the following: given an $n \times n$ array $A$ of positive numbers, find a tiling using at most $p$ rectangles (which means that each array element must be covered by some rectangle and no two rectangles must overlap) that minimizes the maximum weight of any rectangle (the weight of a rectangle is the sum of elements which are covered by it). We prove that it is NP-hard to approximate this problem to within a factor of \textbf{1$\frac{1}{3}$} (the previous best result was $1\frac{1}{4}$).
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