A polynomial time approximation scheme for the square packing problem

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 . We present a polynomial time approximation scheme for this problem, that for any value ε>∈0 finds and packs a subset Q′⊆Q of profit at least (1-ε) 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+ε achieved by Harren's algorithm. © 2008 Springer-Verlag Berlin Heidelberg.