  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 $1\frac{1}{4}$).
