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Approximation Schemes for the Generalized Extensible Bin Packing Problem
- Source :
- Algorithmica. 84:325-343
- Publication Year :
- 2021
- Publisher :
- Springer Science and Business Media LLC, 2021.
-
Abstract
- We present a new generalization of the extensible bin packing with unequal bin sizes problem. In our generalization the cost of exceeding the bin size depends on the index of the bin and not only on the amount in which the size of the bin is exceeded. This generalization does not satisfy the assumptions on the cost function that were used to present the existing polynomial time approximation scheme (PTAS) for the extensible bin packing with unequal bin sizes problem. In this work, we show the existence of an efficient PTAS (EPTAS) for this new generalization and thus in particular we improve the earlier PTAS for the extensible bin packing with unequal bin sizes problem into an EPTAS. Our new scheme is based on using the shifting technique followed by a solution of polynomial number of $n$-fold programming instances. In addition, we present an asymptotic fully polynomial time approximation scheme (AFPTAS) for the related bin packing type variant of the problem.
- Subjects :
- FOS: Computer and information sciences
Discrete mathematics
General Computer Science
Generalization
Bin packing problem
Applied Mathematics
Function (mathematics)
Type (model theory)
Extensibility
Bin
Polynomial-time approximation scheme
Computer Science Applications
Scheme (mathematics)
Computer Science - Data Structures and Algorithms
Data Structures and Algorithms (cs.DS)
Computer Science::Data Structures and Algorithms
Mathematics
Subjects
Details
- ISSN :
- 14320541 and 01784617
- Volume :
- 84
- Database :
- OpenAIRE
- Journal :
- Algorithmica
- Accession number :
- edsair.doi.dedup.....8deb16e1843dc7217298e7a3b5fe33bd