Abstract
In the d-dimensional online bin packing problem, d-dimensional cubes of positive sizes no larger than 1 are presented one by one to be assigned to positions in d-dimensional unit cube bins. In this work, we provide improved upper bounds on the asymptotic competitive ratio for square and cube bin packing problems, where our bounds do not exceed 2.0885 and 2.5735 for square and cube packing, respectively. To achieve these results, we adapt and improve a previously designed harmonic-type algorithm, and apply a different method for defining weight functions. We detect deficiencies in the state-of-the-art results by providing counter-examples to the current best algorithms and their analysis, where the claimed bounds were 2.1187 for square packing and 2.6161 for cube packing.
| Original language | English |
|---|---|
| Pages (from-to) | 1415-1458 |
| Number of pages | 44 |
| Journal | Algorithmica |
| Volume | 85 |
| Issue number | 5 |
| DOIs | |
| State | Published - May 2023 |
Bibliographical note
Publisher Copyright:© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
Keywords
- Bin packing
- Competitive analysis
- Cube packing
- Square packing
ASJC Scopus subject areas
- General Computer Science
- Computer Science Applications
- Applied Mathematics