A combinatorial characterization of higher-dimensional orthogonal packing

TL;DR

This paper introduces a novel graph-theoretical framework for modeling higher-dimensional orthogonal packings, enabling more efficient algorithms by leveraging combinatorial structures and graph properties.

Contribution

It presents the first combinatorial characterization of feasible packings that facilitates a branch-and-bound approach for higher-dimensional packing problems.

Findings

Effective modeling of packings using graph theory

Enhanced branch-and-bound algorithm performance

Applicable to various practical packing problems

Abstract

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.