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Hybrid next-fit algorithm for the two-dimensional rectangle bin-packing problem

Hybrid Next-Fit Algorithmus für das zweidimensionale Rechteck-Packungsproblem

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Abstract

We present a new approximation algorithm for the two-dimensional bin-packing problem. The algorithm is based on two one-dimensional bin-packing algorithms. Since the algorithm is of next-fit type it can also be used for those cases where the output is required to be on-line (e. g. if we open an new bin we have no possibility to pack elements into the earlier opened bins). We give a tight bound for its worst-case and show that this bound is a parameter of the maximal sizes of the items to be packed. Moreover, we also present a probabilistic analysis of this algorithm.

Zusammenfassung

Wir geben einen neuen Näherungs-Algorithmus für das zweidimensionale Packungsproblem an. Er beruht auf zwei eindimensionalen Packungsalgorithmen. Da der Algorithmus von next-fit Typ ist, kann er auch in solchen Fällen benutzt werden, wo die Ausgabe on-line sein muß (d. h. sobald wir einen neuen Behälter eröffnen, haben wir keine Möglichkeit, Elemente in früher geöffnete Behälter zu packen). Wir geben eine gute Schranke im schlechtesten Fall an und zeigen, daß diese Schranke von der Maximalgröße der gepackten Rechtecke abhängt. Schließlich untersuchen wir noch das mittlere Verhalten des Algorithmus.

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Authors and Affiliations

  1. Faculteit der Economische Wetenschappen, Erasmus Universiteit, Postbus 1738, NL-3000 DR, Rotterdam, The Netherlands

    J. B. G. Frenk

  2. Kalmár Laboratory of Cybernetics, József Attila University, Árpád tér 2, H-6720, Szeged, Hungary

    G. Galambos

Authors
  1. J. B. G. Frenk
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  2. G. Galambos
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Frenk, J.B.G., Galambos, G. Hybrid next-fit algorithm for the two-dimensional rectangle bin-packing problem. Computing 39, 201–217 (1987). https://doi.org/10.1007/BF02309555

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  • DOI: https://doi.org/10.1007/BF02309555

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