Two- and three-dimensional parametric packing

We present approximation algorithms for the two- and three-dimensional bin packing problems and the three-dimensional strip packing problem. We consider the special case of these problems in which a parameter m (a positive integer) is given, indicating that each of the dimensions of the items to be packed is at most 1/m of the corresponding dimension of the recipient. We analyze the asymptotic performance of these algorithms and exhibit bounds that, to our knowledge, are the best known for this special case.