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Citation

Allen SD & Burke E (2012) Data structures for higher-dimensional rectilinear packing. INFORMS Journal on Computing, 24 (3), pp. 457-470. https://doi.org/10.1287/ijoc.1110.0464

Abstract
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.

Keywords
computers; data structure; cutting stock; combinatorial optimization

Journal
INFORMS Journal on Computing: Volume 24, Issue 3