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Higher-Dimensional Packing with Order Constraints

Sandor P. Fekete·Ekkehard Koehler·Juergen Teich
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Abstract

We present a first exact study on higher-dimensional packing problems with order constraints. Problems of this type occur naturally in applications such as logistics or computer architecture and can be interpreted as higher-dimensional generalizations of scheduling problems. Using graph-theoretic structures to describe feasible solutions, we develop a novel exact branch-and-bound algorithm. This extends previous work by Fekete and Schepers; a key tool is a new order-theoretic characterization of feasible extensions of a partial order to a given complementarity graph that is tailor-made for use in a branch-and-bound environment. The usefulness of our approach is validated by computational results.

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Sandor P. Fekete, Ekkehard Koehler, Juergen Teich. 2005-07-28. Higher-Dimensional Packing with Order Constraints. https://arxiv.org/abs/cs/0308006

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