A combinatorial characterization of higher-dimensional orthogonal packing
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Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Previous efforts for exact algorithms have been unable to avoid structural problems that appear for instances in two- or higher-dimensional space. We present a new approach for modeling packings, using a graph-theoretical characterization of feasible packings. Our characterization allows it to deal with classes of packings that share a certain combinatorial structure, instead of having to consider one packing at a time. In addition, we can make use of elegant algorithmic properties of certain classes of graphs. This allows our characterization to be the basis for a successful branch-and-bound framework.
This is the first in a series of papers describing new approaches to higher-dimensional packing.
21 pages, 8 figures, Latex, to appear in Mathematics of Operations Research
21 pages, 8 figures, Latex, to appear in Mathematics of Operations Research