Approximating Smallest Containers for Packing Three-Dimensional Convex Objects

作     者：Helmut Alt Nadja Scharf 

作者机构：Institut für Informatik Freie Universität Berlin Takustraße 9 14195 Berlin Germany 

出 版 物：《International Journal of Computational Geometry & Applications》 

年 卷 期：2018年第28卷第2期

页      面：111-128页

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：Computational geometry packing approximation algorithm 

摘      要：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 𝒩 𝒫 -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.