Approximate strip packing

We present an 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+ε) of optimal, and has running time polynomial both in n and in 1/ε. It is based on a reduction to fractional bin-packing, and can be performed by 5 stages of guillotine cuts