Optimal packing of 28 equal circles in a unit square -- the first reliable solution

DOI10.1023/B:NUMA.0000049472.75023.0azbMath1077.90056MaRDI QIDQ2387771

Mihály Csaba Markót

Publication date: 5 September 2005

Published in: Numerical Algorithms (Search for Journal in Brave)

zbMATH Keywords

circle packinginterval arithmeticbranch-and-bound methods

Mathematics Subject Classification ID

Polyhedral combinatorics, branch-and-bound, branch-and-cut (90C57) Combinatorial optimization (90C27) Packing and covering in (2) dimensions (aspects of discrete geometry) (52C15) Circle packings and discrete conformal geometry (52C26)

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Interval methods for verifying structural optimality of circle packing configurations in the unit square ⋮ Searching approximate global optimal Heilbronn configurations of nine points in the unit square via GPGPU computing ⋮ Optimal packings of 2,3, and 4 equal balls into a cubical flat 3-torus ⋮ Statistical inference for disordered sphere packings ⋮ Packing, covering and tiling in two-dimensional spaces ⋮ A reliable area reduction technique for solving circle packing problems ⋮ On the packing of fourteen congruent spheres in a cube

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