New bounds for multidimensional packing

New upper and lower bounds are presented for a multidimensional generalization of bin packing called box packing. Several variants of this problem, including bounded space box packing, square packing, variable-sized box packing and resource augmented box packing are also studied. The main results, stated for d = 2, are as follows: a new upper bound of 2.66013 for online box packing, a new 14/9 + ε polynomial time offline approximation algorithm for square packing, a new upper bound of 2.43828 for online square packing, a new lower bound of 1.62176 for online square packing, a new lower bound of 2.28229 for bounded space online square packing and a new upper bound of 2.32571 for online two-sized box packing.