Consecutive ones matrices for multi-dimensional orthogonal packing problems

The multi-dimensional orthogonal packing problem (OPP) is a well studied optimization problem [3,9]. 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. Rotation of items is not allowed. Fekete and Schepers introduced a tuple of interval graphs as data structures to store a feasible packing, and gave a very efficient algorithm. In this paper, we propose a new algorithm using consecutive one matrices as data structures, due to Fulkerson and Gross’s characterization of interval graphs. Computational results are reported, which show its effectiveness.