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| Content Provider | Society for Industrial and Applied Mathematics (SIAM) |
|---|---|
| Author | Sviridenko, Maxim Han, Xin Bansal, Nikhil Iwama, Kazuo Zhang, Guochuan |
| Copyright Year | 2013 |
| Abstract | In the three-dimensional (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 two-dimensional (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 well-known 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 ReĢmila. |
| Starting Page | 579 |
| Ending Page | 592 |
| Page Count | 14 |
| File Format | |
| ISSN | 00975397 |
| DOI | 10.1137/070691607 |
| e-ISSN | 10957111 |
| Journal | SIAM Journal on Computing (SMJCAT) |
| Issue Number | 2 |
| Volume Number | 42 |
| Language | English |
| Publisher | Society for Industrial and Applied Mathematics |
| Publisher Date | 2013-03-28 |
| Access Restriction | Subscribed |
| Subject Keyword | Online algorithms Analysis of algorithms and problem complexity Approximation algorithms harmonic algorithm strip packing Analysis of algorithms bin packing |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics Computer Science |
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