Abstract
Given a set Q of squares with positive profits, the square packing problem is to select and pack a subset of squares of maximum profit into a rectangular bin R. We present a polynomial time approximation scheme for this problem, that for any value Ɛ > 0 finds and packs a subset Q′ ⊆ Q of profit at least (1 - Ɛ)OPT, where OPT is the profit of an optimum solution. This settles the approximability of the problem and improves on the previously best approximation ratio of 5/4 +Ɛ achieved by Harren's algorithm.
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