Comments on the hierarchically structured bin packing problem

Comments on the hierarchically structured bin packing problem

We study the hierarchically structured bin packing problem. In this problem, the items to be packed into bins are at the leaves of a tree. The objective of the packing is to minimize the total number of bins into which the descendants of an internal node are packed, summed over all internal nodes. W...

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Veröffentlicht in:Information processing letters 2015-02, Vol.115 (2), p.306-309
Hauptverfasser: Lambert, Thomas, Marchal, Loris, Uçar, Bora
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
Approximation
Approximation algorithms
Bin packing
Bins
Combinatorics
Computer Science
Data processing
Data Structures and Algorithms
Discrete Mathematics
Mathematical analysis
Mathematics
NP-hardness
Operations research
Optimization
Packing problem
Studies
Trees
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Beschreibung
Zusammenfassung:We study the hierarchically structured bin packing problem. In this problem, the items to be packed into bins are at the leaves of a tree. The objective of the packing is to minimize the total number of bins into which the descendants of an internal node are packed, summed over all internal nodes. We investigate an existing algorithm and make a correction to the analysis of its approximation ratio. Further results regarding the structure of an optimal solution and a strengthened inapproximability result are given. •No APTAS for hierarchically structured bin packing problem with non-uniform weights.•A condition for a known heuristic to have 3/2 approximation guarantee.•Best post-order is not always best.
ISSN:0020-0190
1872-6119
DOI:10.1016/j.ipl.2014.10.001