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Price-and-verify: a new algorithm for recursive circle packing using Dantzig–Wolfe decomposition
Annals of Operations Research, 2017Packing rings into a minimum number of rectangles is an optimization problem which appears naturally in the logistics operations of the tube industry. It encompasses two major difficulties, namely the positioning of rings in rectangles and the recursive ...
Ambros M. Gleixner +3 more
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International Conference Nanotechnology for Instrumentation and Measurement, 2018
In this paper, we present a new algorithm for the fast and efficient solution of the Packing problem in two dimensions. The packing problem consists in finding the best arrangement of objects (many geometrical forms) in a specific space called container ...
Félix Martínez-Rios +2 more
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In this paper, we present a new algorithm for the fast and efficient solution of the Packing problem in two dimensions. The packing problem consists in finding the best arrangement of objects (many geometrical forms) in a specific space called container ...
Félix Martínez-Rios +2 more
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The Voronoi Cell in a saturated Circle Packing and an elementary proof of Thue´s theorem
, 2019The famous Kepler conjecture has a less spectacular, two-dimensional equivalent: The theorem of Thue states that the densest circle packing in the Euclidean plane has a hexagonal structure.
Max Leppmeier
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Efficiently Packing Circles into a Larger Containing Circle
2010The circles packing problem consists in placing a set of circles into a larger containing circle without overlap. The objective is to determine the smallest radius of the containing circle as well as the coordinates of the center of each given circle. Lacking powerful optimization method is the key obstacle to solve this problem.
Jingfa Liu, Yali Wang, Jinji Pan
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The Densest Packing of 19 Congruent Circles in a Circle
Geometriae Dedicata, 1999It is proved that the densest packing of 19 congruent circles in a circle is the easy conjectured one: a circle in the center, six touching it around and twelve still around as vertices of a regular dodecagon. The proof uses a Bateman-Erdős approach (originally designed for finding the Besicovitch number \(\beta_2=19\)) and author's useful geometrical ...
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PACKING EQUAL CIRCLES IN A SQUARE
Studia Scientiarum Mathematicarum Hungarica, 2000The problem of maximizing the radius of n equal circles that can be packed into a given square is a well-known geometrical problem.It is equivalent to the problem of scattering n points in a square so that the minimum distance between any two points is as large as possible.The optimal packings of at most 20 circles are known,and probably best packings ...
Ament, P., Blind, G.
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The character of Thurston’s circle packings
Science China MathematicszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ge, Huabin, Lin, Aijin
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A Simulated Annealing approach for the Circle Bin Packing Problem with Rectangular Items
Computers & industrial engineering, 2023Kevin Tole +3 more
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Packing of Incongruent Circles on the Sphere
Monatshefte f�r Mathematik, 2001The main result of this paper is an upper bound to the weighted density \(D\) of a packing of circles on the sphere, with radii selected from a given set \(\{r_{1},\ldots ,r_{n}\}\), namely \(D\leq \max \{D(r_{i},r_{j},r_{k})\), \(1\leq i\leq j\leq k\leq n\}\), where \(D(r_{i},r_{j},r_{k})\) denotes the weighted density of three mutually touching ...
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Positioning of new mobile tower using Circle Packing Problem
Evolutionary IntelligenceYogesh Kumar, Kusum Deep
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