Bin packing with cardinality constraints is a basic bin packing problem. In the online version with the parameter k≥2, items having sizes in (0,1] associated with them are presented one by one to be packed into unit capacity bins, such that the capacities of bins are not exceeded, and no bin receives more than k items. We resolve the online problem and prove a lower bound of 2 on the overall asymptotic competitive ratio. Additionally, we significantly improve the known lower bounds on the asymptotic competitive ratio for every specific value of k. The novelty of our constructions is based on full adaptivity that creates large gaps between item sizes. Last, we show a lower bound strictly larger than 2 on the asymptotic competitive ratio of the online 2-dimensional vector packing problem, where no such lower bound was known even for fixed high dimensions.
Bibliographical noteFunding Information:
Supported by the EU-funded Hungarian grant EFOP-3.6.2-16-2017-00015 and by National Research, Development and Innovation Office NKFIH under the grant SNN 129178.Supported by Szechenyi 2020 under the EFOP-3.6.1-16-2016-00015 and by National Research, Development and Innovation Office NKFIH under the grant SNN 116095.
© 2020 Elsevier Inc.
- Bin packing
- Cardinality constraints
- Competitive ratio
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Networks and Communications
- Computational Theory and Mathematics
- Applied Mathematics