Approximating Smallest Containers for Packing Three-Dimensional Convex Objects

Authors Helmut Alt, Nadja Scharf

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Helmut Alt
Nadja Scharf

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Helmut Alt and Nadja Scharf. Approximating Smallest Containers for Packing Three-Dimensional Convex Objects. In 27th International Symposium on Algorithms and Computation (ISAAC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 64, pp. 11:1-11:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


We investigate the problem of computing a minimum-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 packing 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 minimum volume containers for the objects described.
  • computational geometry
  • packing
  • approximation algorithm


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