In the d-dimensional online bin packing problem, hyper-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 the analysis, where the claimed bounds were 2.1187 for square packing and 2.6161 for cube packing.
|Title of host publication||Algorithms and Data Structures - 17th International Symposium, WADS 2021, Proceedings|
|Editors||Anna Lubiw, Mohammad Salavatipour|
|Publisher||Springer Science and Business Media Deutschland GmbH|
|Number of pages||14|
|State||Published - 2021|
|Event||17th International Symposium on Algorithms and Data Structures, WADS 2021 - Virtual, Online|
Duration: 9 Aug 2021 → 11 Aug 2021
|Name||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|Conference||17th International Symposium on Algorithms and Data Structures, WADS 2021|
|Period||9/08/21 → 11/08/21|
Bibliographical notePublisher Copyright:
© 2021, Springer Nature Switzerland AG.
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Science (all)