# Approximation Algorithm for Multiple Strip Packing

2 MOAIS - PrograMming and scheduling design fOr Applications in Interactive Simulation
Inria Grenoble - Rhône-Alpes, LIG - Laboratoire d'Informatique de Grenoble
3 Theory of Parallelism
Department of Computer Science, CAU - Christian-Albrechts-Universität zu Kiel
Abstract : In this paper 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 previous 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.
Type de document :
Communication dans un congrès
WAOA'2009: 7th Workshop on Approximation and Online Algorithms, Sep 2009, Copenhague, Denmark. Springer, 5893, pp.37-48, 2009, LNCS. 〈10.1007/978-3-642-12450-1_4〉
Liste complète des métadonnées

Littérature citée [16 références]

https://hal.archives-ouvertes.fr/hal-00738614
Contributeur : Marin Bougeret <>
Soumis le : jeudi 4 octobre 2012 - 16:27:37
Dernière modification le : mercredi 11 avril 2018 - 01:54:30
Document(s) archivé(s) le : samedi 5 janvier 2013 - 03:59:53

### Fichier

paper.pdf
Fichiers produits par l'(les) auteur(s)

### Citation

Marin Bougeret, Pierre-Francois Dutot, Klaus Jansen, Christina Otte, Denis Trystram. Approximation Algorithm for Multiple Strip Packing. WAOA'2009: 7th Workshop on Approximation and Online Algorithms, Sep 2009, Copenhague, Denmark. Springer, 5893, pp.37-48, 2009, LNCS. 〈10.1007/978-3-642-12450-1_4〉. 〈hal-00738614〉

### Métriques

Consultations de la notice

## 462

Téléchargements de fichiers