Serial Symmetrical Relocation Algorithm for the Equal Sphere Packing Problem

Details Serial Symmetrical Relocation Algorithm for the Equal Sphere Packing Problem Serial Symmetrical Relocation Algorithm for the Equal Sphere Packing Problem

2012-02-19

arxiv.org/abs/1202.4149v1

Computer Science

Discrete Mathematics

19 pages, 3 figures, it was conjectured that a sphere of radius 5 can contain at most 67 spheres of radius 1. Now 68 sphere of

Scientific paper

For dealing with the equal sphere packing problem, we propose a serial symmetrical relocation algorithm, which is effective in terms of the quality of the numerical results. We have densely packed up to 200 equal spheres in spherical container and up to 150 equal spheres in cube container. All results are rigorous because of a fake sphere trick. It was conjectured impossible to pack 68 equal spheres of radius 1 into a sphere of radius 5. The serial symmetrical relocation algorithm has proven wrong this conjecture by finding one such packing.

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