A General Framework for Bounds for Higher-Dimensional Orthogonal Packing Problems

Title: A General Framework for Bounds for Higher-Dimensional Orthogonal Packing Problems

Research Question: How can we develop a general framework for obtaining better and easier-to-generalize bounds for higher-dimensional orthogonal packing problems?

Methodology: The authors propose a new approach for obtaining classes of lower bounds for higher-dimensional packing problems. They introduce the concept of dual feasible functions and use these functions to construct conservative scales, which serve as the basis for lower bounds.

Results: The authors present a number of lower bounds for various higher-dimensional packing problems. They show that their approach improves and simplifies several well-known bounds from previous literature and provides an easy framework for proving the correctness of new bounds.

Implications: The new approach presented in this paper provides a more general and efficient way to obtain bounds for higher-dimensional orthogonal packing problems. This can lead to improved algorithms and better solutions for a wide range of practical applications, such as packing, cutting, and scheduling problems.

Link to Article: https://arxiv.org/abs/0402044v1 Authors: arXiv ID: 0402044v1