A Near-Optimal Solution to a Two-Dimensional Cutting Stock Problem

We present an asymptotic fully polynomial approximation scheme for strip-packing, or packing rectangles into a rectangle of fixed width and minimum height, a classical NP-hard cutting-stock problem. The algorithm finds a packing of n rectangles whose total height is within a factor of (1 + ffl) of optimal (up to an additive term), and has running time polynomial both in n and in 1=ffl. It is based on a reduction to fractional bin-packing