Title: An asymptotic worst case analysis of the effectiveness of the Harmonic 3D-shelf algorithm for online 3D-strip packing

Authors: Massimiliano Caramia, Stefano Giordani

Addresses: Dipartimento di Ingegneria dell'Impresa, University of Rome 'Tor Vergata', Via del Politecnico 1, Rome 00133, Italy. ' Dipartimento di Ingegneria dell'Impresa, University of Rome 'Tor Vergata', Via del Politecnico 1, Rome 00133, Italy

Abstract: It is well known that shelf algorithms are used to pack items into strips. Harmonic shelf algorithms represent a particular subclass of these algorithms with which an asymptotic worst case analysis has been conducted on two-dimensional (2D) strip packing. In this paper, we consider the 3D-strip packing problem and analyse the effectiveness of the Harmonic 3D-shelf algorithm in terms of the ratio between the wasted volume inside the used portion of the strip and the total size of the latter, and we show that this algorithm is capable to pack items so that the asymptotic worst case value of this ratio comes arbitrarily close to 3/4. The results come from an extension of the 2D case.

Keywords: online 3D strip packing; online algorithms; worst case analysis; harmonic shelf algorithms.

DOI: 10.1504/IJMOR.2010.032722

International Journal of Mathematics in Operational Research, 2010 Vol.2 No.3, pp.336 - 346

Published online: 17 Apr 2010 *

Full-text access for editors Access for subscribers Purchase this article Comment on this article