2013
A Harmonic Algorithm for the 3D Strip Packing Problem
Publication
Publication
SIAM Journal on Computing , Volume 42  Issue 2 p. 579 592
In the threedimensional (3D) strip packing problem, we are given a set of 3D rectangular items and a 3D box $B$. The goal is to pack all the items in $B$ such that the height of the packing is minimized. We consider the most basic version of the problem, where the items must be packed with their edges parallel to the edges of $B$ and cannot be rotated. Building upon Caprara's work for the twodimensional (2D) bin packing problem, we obtain an algorithm that, given any $\epsilon>0$, achieves an approximation of $T_{\infty}+\epsilon\approx1.69103+\epsilon$, where $T_{\infty}$ is the wellknown number that occurs naturally in the context of bin packing. Our key idea is to establish a connection between bin packing solutions for an arbitrary instance $I$ and the strip packing solutions for the corresponding instance obtained from $I$ by applying the harmonic transformation to certain dimensions. Based on this connection, we also give a simple alternate proof of the $T_{\infty}+\epsilon$ approximation for 2D bin packing due to Caprara. In particular, we show how his result follows from a simple modification of the asymptotic approximation scheme for 2D strip packing due to Kenyon and Rémila.
Additional Metadata  

SIAM  
SIAM Journal on Computing  
Organisation  Computer Security 
Bansal, N, Han, X, Iwama, K, Sviridenko, M, & Zhang, G. (2013). A Harmonic Algorithm for the 3D Strip Packing Problem. SIAM Journal on Computing, 42(2), 579–592.
