A Polynomial Time Approximation Scheme for the Square Packing Problem

Given a set Q of squares with positive pro ts, the square packing problem is to select and pack a subset of squares of maximum pro t into a rectangular bin R. We present a polynomial time approximation scheme for this problem, that for any value > 0 nds and packs a subset Q 0 Q of pro t at least (1 ? )OP T , where OP T is the pro t of an optimum solution. This settles the approximability of the problem and improves on the previously best approximation ratio of 5=4 + achieved by Harren's algorithm.

• Type: Conference
• Year: 2008
• Where: IPCO
• Authors: Klaus Jansen, Roberto Solis-Oba
• Keywords: IPCO 2008, Optimization, Polynomial Time Approximation Scheme, Positive Pro Ts, Square Packing Problem