Interval methods for verifying structural optimality of circle packing configurations in the unit square
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Publication:861900
DOI10.1016/j.cam.2005.08.039zbMath1107.52013OpenAlexW2135620139MaRDI QIDQ861900
Publication date: 2 February 2007
Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cam.2005.08.039
Nonlinear programming (90C30) Interval and finite arithmetic (65G30) Packing and covering in (2) dimensions (aspects of discrete geometry) (52C15) Circle packings and discrete conformal geometry (52C26)
Related Items (9)
Minimal surface convex hulls of spheres ⋮ A literature review on circle and sphere packing problems: models and methodologies ⋮ Greedy vacancy search algorithm for packing equal circles in a square ⋮ Rigorous packing of unit squares into a circle ⋮ Optimal packings of 2,3, and 4 equal balls into a cubical flat 3-torus ⋮ Cutting ellipses from area-minimizing rectangles ⋮ On tackling reverse convex constraints for non-overlapping of unequal circles ⋮ Symplectic embedding problems, old and new ⋮ Techniques and results on approximation algorithms for packing circles
Uses Software
Cites Work
- Densest packings of equal circles in a square
- Packing up to 50 equal circles in a square
- Some new structures for the ``equal circles packing in a square problem
- More optimal packings of equal circles in a square
- Introduction to global optimization
- Repeated patterns of dense packings of equal disks in a square
- Optimal packing of 28 equal circles in a unit square -- the first reliable solution
- Interval Methods for Systems of Equations
- A New Verified Optimization Technique for the "Packing Circles in a Unit Square" Problems
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