# ASTEC 2009 Workshop/Summer school on Algorithms and Techniques for Scheduling on Clusters and Grids

## June, 02 - 05 2009, Centre CNRS "Les Plantiers"

### Approximation algorithms for Muliple Strip Packing

SpeakerChristina Otte

Co-authorK. Jansen

Approximation algorithms for Muliple Strip Packing

We study the Multiple Strip Packing (MSP) problem, a generalization of the well-known Strip Packing problem. For a given set of rectangles, $r_1,\ldots,r_n$, with heights and widths $\le 1$, the goal is to find a non-overlapping orthogonal packing without rotations into $k\in\mathbb{N}$ strips $[0,1]\times[0,\infty)$, minimizing the maximum of the heights. We present an approximation algorithm with absolute ratio $2$, which is the best possible, unless ${\cal P}={\cal NP}$, and an improvement of the further best result with ratio $2+\EPS$. Furthermore we present simple shelf-based algorithms with short running-time and an AFPTAS for MSP. Since MSP is strongly ${\cal NP}$-hard, an FPTAS is ruled out and an AFPTAS is also the best possible result in the sense of approximation theory.

slides(pdf)