Abstract
We study the following square packing problem: Given a set Q of squares with positive profits, the goal is to pack a subset of Q into a rectangular bin $\mathcal R$ so that the total profit of the squares packed in $\mathcal R$ is maximized. Squares must be packed so that their sides are parallel to those of $\mathcal R$. We present a polynomial time approximation scheme for the problem, which for any value $\epsilon > 0$ finds and packs a subset $Q' \subseteq Q$ of profit at least $(1-\epsilon) OPT$, where $OPT$ is the profit of an optimum solution.
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