On the multidimensional vector bin packing

J. Csirik, J. B G Frenk, M. Labbe, S. Zhang

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

Abstract

The multidimensional vector bin packing problem consists in packing m-dimensional items into a minimum number of m-dimensional bins with unit capacity in each of the m dimensions in such a way that the sum of each coordinate of the items received by any bin is not larger than one. We improve the lower bound of the First-Fit-Decreasing heuristic when m≥5 and odd, and prove that this heuristic is optimal when m = 2 if each item has at least one coordinate larger than 1/2. Finally, if this last condition holds and m≥3, we show that the problem remains NP-hard.

Original languageEnglish (US)
Pages (from-to)361-369
Number of pages9
JournalActa Cybernetica
Volume9
Issue number4
StatePublished - Dec 1 1990

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