Packing and Covering

By G. Tóth. Handbook of Discrete and Computational Geometry, 2nd Ed., 2004

313 citations recorded by the source corpus.

Subfields: Electrical and Electronic Engineering, Industrial and Manufacturing Engineering

View Paper: https://www.semanticscholar.org/paper/f5739c2acbb0c194b456bf2858dc2ff6922a198d

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Citations in the corpus

The Crystallization Conjecture: A Review (2015, background): “A proof was then proposed in 1940 by Tóth [144, 49].”
Covering the Sphere by Equal Spherical Balls (2003, background): “Kuperberg [13]), and the optimal arrangement is known in many cases.”
Mean-field theory of hard sphere glasses and jamming (2008, background): “erred to the original literature and to the existing excellent books and reviews, e.g. (Alexander, 1998; Aste, 2005; Conway and Sloane, 1993; Goldbart et al., 2005; Krauth, 2006; Liu and Nagel, 2001; Rogers, 1964; Torquato, 2002). Similarly, many excellent general books and reviews on the physics of”
Achieving 1/2 log (1+SNR) on the AWGN channel with lattice encoding and decoding (2004, background): “As for a coarse (shaping) lattice , we use a lattice that is simultaneously Rogers-good and Poltyrev-good.”
Lattice coding and decoding achieve the optimal diversity-multiplexing tradeoff of MIMO channels (2004, background): “Such lattice sequences exist, as shown in [28] (see also [29]).”
Bandit Algorithms (2020, background): “The main reference is by Rogers [1964], which by now is a little old, but still interesting.”
A candidate for the densest packing with equal balls in Thurston geometries (2012, background): “ conjectured that in an n-dimensional space of constant curvature the density of packing balls of radius r can not exceed dn(r). This conjecture has been proved by C. Rogers in the Euclidean space En [18]. The 2-dimensional A candidate to the densest packing with equal balls... 3 spherical case was ”
The gradual covering problem (2004, background): “An early report on the covering problem is [18].”
Lattices which are good for (almost) everything (2003, methodology): “His proof utilizes the techniques of Rogers [6].”
Efficient detection of motion patterns in spatio-temporal data sets (2004, background): “By the pigeonhole principle, one of the radius-r discs must be intersected by at least 7m/7 = m half-lines [20].”