Higher-Dimensional Orthogonal Packing

Title: Higher-Dimensional Orthogonal Packing

Research Question: How can we develop an efficient method for solving higher-dimensional orthogonal packing problems, which are known to be NP-complete and difficult to solve?

Methodology: The authors propose a new approach for modeling higher-dimensional packings using a graph-theoretical characterization. This characterization allows them to deal with classes of packings that share a certain combinatorial structure, instead of having to consider one packing at a time. They also make use of elegant algorithmic properties of certain classes of graphs, which helps in developing a successful branch-and-bound framework.

Results: The authors present a new approach for modeling packings, using a graph-theoretical characterization of feasible packings. They demonstrate that their characterization allows them to deal with classes of packings that share a certain combinatorial structure, and that they can make use of elegant algorithmic properties of certain classes of graphs. They also develop a successful branch-and-bound framework based on their characterization.

Implications: The authors' work has significant implications for the field of combinatorial optimization. Their new approach for modeling higher-dimensional packings provides a more efficient method for solving these problems, which are known to be NP-complete and difficult to solve. Their work opens up new possibilities for solving a wide range of practical problems, such as packing, cutting, and scheduling, in two or higher dimensions.

Conclusion: In conclusion, the authors have developed a new approach for modeling higher-dimensional orthogonal packings using a graph-theoretical characterization. Their characterization allows them to deal with classes of packings that share a certain combinatorial structure, and they can make use of elegant algorithmic properties of certain classes of graphs. Their work has significant implications for the field of combinatorial optimization, providing a more efficient method for solving higher-dimensional orthogonal packing problems.

Link to Article: https://arxiv.org/abs/0310032v1 Authors: arXiv ID: 0310032v1