Covering and packing with spheres by diagonal distortion in R^n

H. Edelsbrunner, M. Kerber, in:, C. Calude, G. Rozenberg, A. Salomaa (Eds.), Rainbow of Computer Science, Springer, 2011, pp. 20–35.

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Book Chapter | Published | English
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LNCS
Abstract
We address the problem of covering ℝ n with congruent balls, while minimizing the number of balls that contain an average point. Considering the 1-parameter family of lattices defined by stretching or compressing the integer grid in diagonal direction, we give a closed formula for the covering density that depends on the distortion parameter. We observe that our family contains the thinnest lattice coverings in dimensions 2 to 5. We also consider the problem of packing congruent balls in ℝ n , for which we give a closed formula for the packing density as well. Again we observe that our family contains optimal configurations, this time densest packings in dimensions 2 and 3.
Publishing Year
Date Published
2011-05-03
Book Title
Rainbow of Computer Science
Volume
6570
Page
20 - 35
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Edelsbrunner H, Kerber M. Covering and packing with spheres by diagonal distortion in R^n. In: Calude C, Rozenberg G, Salomaa A, eds. Rainbow of Computer Science. Vol 6570. Dedicated to Hermann Maurer on the Occasion of His 70th Birthday. Springer; 2011:20-35. doi:10.1007/978-3-642-19391-0_2
Edelsbrunner, H., & Kerber, M. (2011). Covering and packing with spheres by diagonal distortion in R^n. In C. Calude, G. Rozenberg, & A. Salomaa (Eds.), Rainbow of Computer Science (Vol. 6570, pp. 20–35). Springer. https://doi.org/10.1007/978-3-642-19391-0_2
Edelsbrunner, Herbert, and Michael Kerber. “Covering and Packing with Spheres by Diagonal Distortion in R^n.” In Rainbow of Computer Science, edited by Cristian Calude, Grzegorz Rozenberg, and Arto Salomaa, 6570:20–35. Dedicated to Hermann Maurer on the Occasion of His 70th Birthday. Springer, 2011. https://doi.org/10.1007/978-3-642-19391-0_2.
H. Edelsbrunner and M. Kerber, “Covering and packing with spheres by diagonal distortion in R^n,” in Rainbow of Computer Science, vol. 6570, C. Calude, G. Rozenberg, and A. Salomaa, Eds. Springer, 2011, pp. 20–35.
Edelsbrunner H, Kerber M. 2011. Covering and packing with spheres by diagonal distortion in R^n. Rainbow of Computer Science. Dedicated to Hermann Maurer on the Occasion of His 70th Birthday, LNCS, vol. 6570. 20–35.
Edelsbrunner, Herbert, and Michael Kerber. “Covering and Packing with Spheres by Diagonal Distortion in R^n.” Rainbow of Computer Science, edited by Cristian Calude et al., vol. 6570, Springer, 2011, pp. 20–35, doi:10.1007/978-3-642-19391-0_2.
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