An n-tet graph approach for non-guillotine packings of n-dimensional boxes into an n-container

Abstract In this paper we propose a simple recursive uniform algorithm for the problem of packing n -dimensional boxes into an n -container. We are particularly concerned about the special case n =3 where the boxes can be packed in a given subset of their six possible positionings. Our method studies symmetries in the packings by the use of an ordered set of three directed graphs with the same edges (a 3- tet or triad ) and induced smaller structures of the same kind named minors . With the method, degeneracy and symmetry issues, which curtail the implicit enumeration to practically acceptable running times, become transparent. In order to illustrate the performance of the algorithm, computational results from solving randomly generated 3-D examples are presented and compared with the ones of a layers and knapsack approach. The present study has real world applications for the problems of pallet and container loading.

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