Abstract
The multidimensional vector bin packing problem consists in packing m-dimensional items into a minimum number of m-dimensional bins with unit capacity in each of the m dimensions in such a way that the sum of each coordinate of the items received by any bin is not larger than one. We improve the lower bound of the First-Fit-Decreasing heuristic when m≥5 and odd, and prove that this heuristic is optimal when m = 2 if each item has at least one coordinate larger than 1/2. Finally, if this last condition holds and m≥3, we show that the problem remains NP-hard.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 361-369 |
| Number of pages | 9 |
| Journal | Acta Cybernetica |
| Volume | 9 |
| Issue number | 4 |
| State | Published - Dec 1 1990 |