Consecutive Ones Matrices for Multi-dimensional Orthogonal Packing Problems

Authors:
Cédric Joncour;Arnaud Pêcher
Affiliations:
IMB/INRIA Bordeaux - Sud-Ouest, University of Bordeaux, Talence Cedex, France 33405;Labri, University of Bordeaux, Talence Cedex, France 33405
Venue:
Journal of Mathematical Modelling and Algorithms
Year:
2012

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Abstract

The multi-dimensional orthogonal packing problem (OPP) is a well studied decisional problem. Given a set of items with rectangular shapes, the problem is to decide whether there is a non-overlapping packing of these items in a rectangular bin. The rotation of items is not allowed. A powerful caracterization of packing configurations by means of interval graphs was recently introduced. In this paper, we propose a new algorithm using consecutive ones matrices as data structure. This new algorithm is then used to solve the two-dimensional orthogonal knapsack problem. Computational results are reported, which show its effectiveness.