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 comparability 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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Fekete, S.P., Köhler, E., Teich, J. (2001). Higher-Dimensional Packing with Order Constraints. In: Dehne, F., Sack, JR., Tamassia, R. (eds) Algorithms and Data Structures. WADS 2001. Lecture Notes in Computer Science, vol 2125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44634-6_28
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DOI: https://doi.org/10.1007/3-540-44634-6_28
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