Data Structures for Higher-Dimensional Rectilinear Packing

This paper presents an abstract data type (ADT) for producing higher-dimensional rectilinear packings using constructive methods, the Skyline ADT. Furthermore, a novel method and several approaches from the literature are presented in the form of concrete implementations of the presented ADT. Formal definitions of two three-dimensional packing problems are given, the concept of gaps is explained, and the polynomial growth worst-case behaviour of gaps is shown. The complexity of both the best-fit algorithm and implementations of the ADT are presented, and comparative runtime speeds are analysed over a range of data sets from the literature.