On Packing Squares with Resource Augmentation: Maximizing the Profit

We consider the problem of packing squares with profits into a bounded square region so as to maximize their total profit. More specifically, given a set L of n squares with positive profits, it is required to pack a subset of them into a unit size square region [0;1℄ [0;1℄ so that the total profit of the squares packed is maximized. For any given positive accuracy ε > 0, we present an algorithm that outputs a packing of a subset of L in the augmented square region [1+ ε℄ [1+ ε℄ with profit value at least (1 ε)OPT(L), where OPT(L) is the maximum profit that can be achieved by packing a subset of L in the unit square. The running time of the algorithm is polynomial in n for fixed ε.