Geodesic
An algorithm for packing balls of two types in a three-dimensional set with a non-euclidean metric
Numerical methods and programming, Tome 21 (2020) no. 2, pp. 152-163

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The problem of packing balls of two types into a closed bounded set in three-dimensional space with the Euclidean metric and a special non-Euclidean metric. It is required to maximize the radius of the balls for a given number of balls of each type and a known ratio of radii. We propose a omputational algorithm based on a combination of the billiard modeling method and the optical-geometric approach employing the fundamental physical principles of Fermat and Huygens. The results of numerical experiments are discussed.
Keywords: optimal packing of balls of different radii; computational algorithm; billiard modeling; optical-geometric method; software package. 
@article{VMP_2020_21_2_a2,
     author = {A. L. Kazakov and A. A. Lempert and Trung Thanh Ta},
     title = {An algorithm for packing balls of two types in a three-dimensional set with a non-euclidean metric},
     journal = {Numerical methods and programming},
     pages = {152--163},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2020_21_2_a2/}
}
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A. L. Kazakov; A. A. Lempert; Trung Thanh Ta. An algorithm for packing balls of two types in a three-dimensional set with a non-euclidean metric. Numerical methods and programming, Tome 21 (2020) no. 2, pp. 152-163. http://geodesic.mathdoc.fr/item/VMP_2020_21_2_a2/