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 [Formula: see text]-hard so that we cannot expect to find polynomial time algorithms to determine the exact solution. 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.
Highlights
The problem of efficiently packing objects without overlap arises in a large variety of contexts
A recent result shows that packing convex polygons under translation into a minimum-area rectangular or convex container can be approximated with ratios 17.45 and 27 respectively [1]
In this work we give the first approximation results for packing three-dimensional convex objects in a minimum-volume container
Summary
The problem of efficiently packing objects without overlap arises in a large variety of contexts. Each job needs a certain amount of given resources and the aim is to minimize under certain constraints this need of resources such as time, space, or number of machines This situation can be described as a problem of packing high-dimensional cuboids into a strip with bounded side lengths. Both problems can be viewed as a given list of objects for which a container of minimum size is wanted. We consider the more general and abstract problem of packing threedimensional convex polyhedra into a minimum volume container All variants of this problem are N P-hard and we will develop constant factor approximation algorithms for some of them. 11:2 Approximating Smallest Containers for Packing Three-Dimensional Convex Objects
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
