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.
Caramia, M., Giordani, S. (2010). An Asymptotic worst case analysis of the effectiveness of the harmonic 3D-shelf algorithm for on-line 3D-strip packing. INTERNATIONAL JOURNAL OF MATHEMATICS IN OPERATIONAL RESEARCH, 2(3), 336-346 [10.1504/IJMOR.2010.032722].
An Asymptotic worst case analysis of the effectiveness of the harmonic 3D-shelf algorithm for on-line 3D-strip packing
CARAMIA, MASSIMILIANO;GIORDANI, STEFANO
2010-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
