MPQ-trees for the orthogonal packing problem

Cédric Joncour 1, 2 Arnaud Pêcher 1, 3 Petru Valicov 3, *
* Corresponding author
1 Realopt - Reformulations based algorithms for Combinatorial Optimization
LaBRI - Laboratoire Bordelais de Recherche en Informatique, IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : Given a set of rectangular items of different sizes and a rectangular container, the aim of the bi-dimensional Orthogonal Packing Problem (OPP-2 for short) is to decide whether there exists a non-overlapping packing of the items in this container. The rotation of items is not allowed. In this paper we present a new exact algorithm for solving OPP-2, based upon the characterization of solutions using interval graphs proposed by Fekete and Schepers. The algorithm uses MPQ-trees, which were introduced by Korte and Möhring to recognize interval graphs.
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Cédric Joncour, Arnaud Pêcher, Petru Valicov. MPQ-trees for the orthogonal packing problem. Journal of Mathematical Modelling and Algorithms, Springer Verlag, 2012, 11 (1), pp.3-22. ⟨10.1007/s10852-011-9159-z⟩. ⟨hal-00611528⟩

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