Competitive Multi-dimensional Dynamic Bin Packing via L-Shape Bin Packing

Abstract

We study d-dimensional dynamic bin packing for general d-dimensional boxes, for d≥2. This problem is a generalization of the bin packing problem in which items may arrive and depart dynamically. Our main result is a 3d-competitive online algorithm. We further study the 2- and 3-dimensional problem closely and improve the competitive ratios. Technically speaking, our d-dimensional result is due to a space efficient offline single bin packing algorithm, which is a variant of d-dimensional NFDH. We introduce an interesting notion of d-dimensional L-shape bin and show that effective offline packing into L-shape bin leads to effective online dynamic packing into unit-sized bins. We also investigate the resource augmentation version of the problem where the online algorithm can use d-dimensional bins of size s1 ×s2 ×⋯×sd for si≥1 while the optimal offline algorithm uses unit-sized bins. We give conditions for the online algorithm to match the performance of the optimal offline algorithm, i.e., 1-competitive.