Approximating Smallest Containers for Packing Three-dimensional Convex Objects
Abstract
We investigate the problem of computing a minimal-volume container for the non-overlapping packing of a given set of three-dimensional convex objects. Already the simplest versions of the problem are NP-hard so that we cannot expect to find exact polynomial time algorithms. We give constant ratio approximation algorithms for packing axis-parallel (rectangular) cuboids under translation into an axis-parallel (rectangular) cuboid as container, for cuboids under rigid motions into an axis-parallel cuboid or into an arbitrary convex container, and for packing convex polyhedra under rigid motions into an axis-parallel cuboid or arbitrary convex container. This work gives the first approximability results for the computation of minimal volume containers for the objects described.
Cite
@article{arxiv.1601.04585,
title = {Approximating Smallest Containers for Packing Three-dimensional Convex Objects},
author = {Helmut Alt and Nadja Scharf},
journal= {arXiv preprint arXiv:1601.04585},
year = {2016}
}