Online algorithms for 1‐space bounded multi dimensional bin packing and hypercube packing

In this paper, we study 1‐space bounded multi‐dimensional bin packing and hypercube packing. A sequence of items arrive over time, each item is a d‐dimensional hyperbox (in bin packing) or hypercube (in hypercube packing), and the length of each side is no more than 1. These items must be packed without overlapping into d‐dimensional hypercubes with unit length on each side. In d‐dimensional space, any two dimensions i and j define a space P ij . When an item arrives, we must pack it into an active bin immediately without any knowledge of the future items, and 90°‐rotation on any plane P ij is allowed.