A Near-optimal Solution to a Two-dimensional Cutting Stock Problem a Near-optimal Solution to a Two-dimensional Cutting Stock Problem 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 xed width and minimum height, a classical NP-hard cutting-stock problem. The algorithm nds a packing of n rectangles whose total height is within a factor of (1 +) of optimal (up to an additive term), and has running time polynomial both in n and in 1==. It is based on a reduction to fractional bin-packing. R esum e Nous pr esentons un sch ema totalement polynomial d'approximation pour la mise en boite de rectangles dans une boite de largeur x ee, avec hauteur mi-nimale, qui est un probleme NP-dur classique, de coupes par guillotine. L'al-gorithme donne un placement des rectangles, dont la hauteur est au plus egale a (1 +) (hauteur optimale) et a un temps d'execution polynomial en n et en 1==. Il utilise une reduction au probleme de la mise en boite fractionaire. Abstract We present an asymptotic fully polynomial approximation scheme for strip-packing, or packing rectangles into a rectangle of xed width and minimum height, a classical N P-hard cutting-stock problem. The algorithm nds a packing of n rectangles whose total height is within a factor of (1 +) of optimal (up to an additive term), and has running time polynomial both in n and in 1==. It is based on a reduction to fractional bin-packing.