γ-Soft packings of rectangles

We consider the problem of packing a set of rectangles into a square. The areas of the rectangles are given while their aspect ratios can be chosen from a given interval [1,γ]. We will show that there is always a feasible solution if the square is at least by a factor ργ:=max⁡{4γ4γ−1,2γ} bigger than the total area of the rectangles. Moreover, we will prove that this bound is tight.