Keywords and Synonyms
Ball packing ; Disk packing
Problem Definition
The sphere packing problem seeks to pack spheres into a given geometric domain. The problem is an instance of geometric packing. Geometric packing is a venerable topic in mathematics. Various versions of geometric packing problems have been studied, depending on the shapes of packing domains, the types of packing objects, the position restrictions on the objects, the optimization criteria, the dimensions, etc. It also arises in numerous applied areas. The sphere packing problem under consideration here finds applications in radiation cancer treatment using Gamma Knife systems. Unfortunately, even very restricted versions of geometric packing problems (e. g., regular-shaped objects and domains in lower dimensional spaces) have been proved to be NP-hard. For example, for congruent packing(i. e., packing copies of the same object), it is known that the 2-D cases of packing fixed-sized congruent squares or disks in...
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© 2008 Springer-Verlag
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Chen, D. (2008). Sphere Packing Problem. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_391
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DOI: https://doi.org/10.1007/978-0-387-30162-4_391
Publisher Name: Springer, Boston, MA
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