Abstract
We solve an open problem in the literature by providing an online algorithm for multidimensional bin packing that uses only bounded space. To achieve this, we introduce a new technique for classifying the items to be packed. We show that our algorithm is optimal among bounded space algorithms for any dimension d > 1. Its asymptotic performance ratio is (∏∞d) d, where ∏∞ ≈1.691 is the asymptotic performance ratio of the one-dimensional algorithm HARMONIC. A modified version of this algorithm for the case where all items are hypercubes is also shown to be optimal. Its asymptotic performance ratio is sublinear in d. Additionally, for the special case of packing squares in two-dimensional bins, we present a new unbounded space online algorithm with asymptotic performance ratio of at most 2.271. We also present an approximation algorithm for the offline problem with approximation ratio of 16/11.
| Original language | English |
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| Pages | 207-216 |
| Number of pages | 10 |
| State | Published - 2004 |
| Externally published | Yes |
| Event | Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms - New Orleans, LA., United States Duration: 11 Jan 2004 → 13 Jan 2004 |
Conference
| Conference | Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms |
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| Country/Territory | United States |
| City | New Orleans, LA. |
| Period | 11/01/04 → 13/01/04 |
ASJC Scopus subject areas
- Software
- General Mathematics