Approximation Algorithms for Circle Packing

156 Pages·2016·1.43 MB·English

Approximation Algorithms for Circle
Packing
Flávio K. Miyazawa
unicamp
São Paulo School of Advanced Science on
Algorithms, Combinatorics and Optimization
São Paulo, SP
July, 2016
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Contents
Circle Packing Problems
Basic Algorithms
Circle Bin Packing
Bounded Space Online Bin Packing
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Colaborators and references
Main references
• F. K. Miyazawa, L. L. C. Pedrosa, R. C. S. Schouery, M. Sviridenko,
Y. Wakabayashi. Polynomial-Time Approximation Schemes for Circle
and Other Packing Problems. Algorithmica. To appear.
• P. H. Hokama, F. K. Miyazawa and R. C. S. Schouery. A bounded
space algorithm for online circle packing. Information Processing
Letters, 116, p. 337-342, 2016.
This work also obtained collaboration from Lehilton L. C. Pedrosa,
Maxim Sviridenko, Rafael C. S. Schouery, Pedro H. Hokama and
Yoshiko Wakabayashi.
My thanks to Lehilton Pedrosa and Rafael Schouery that also
contributed to part of these slides. This work obtained support from
CNPq, FAPESP, UNICAMP, USP.
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CirclePackingProblems
Circle Packing Problems
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CirclePackingProblems
Packings
Given:
(cid:73) A list of geometrical items L and bins B
(cid:73) Obtain a good packing of items in L into bin B ∈ B
(cid:73) The inner region of two packed items cannot overlap
(cid:73) Each packed item must be totally contained in the bin
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CirclePackingProblems
Problems
Circle Strip Packing
(cid:73) Input: List of circles L = (c ,...,c )
1 n
(cid:73) Output: Packing of L into a rectangle of width 1 and
minimum height.
Minimize
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CirclePackingProblems
Problems
Circle Bin Packing
(cid:73) Input: List of circles L = (c ,...,c )
1 n
(cid:73) Output: Packing of L into the minimum number of unit
bins.
Minimize
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CirclePackingProblems
Some Applications
(cid:73) Cutting and Packing of circular items
(cid:73) Transportation of tubes, cilinders,...
(cid:73) Cable assembly/allocations
(cid:73) Tree plantation
(cid:73) Origami design
(cid:73) Marketing
(cid:73) Cylinder pallet assembly
(cid:73) ...
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CirclePackingProblems
Marketing
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CirclePackingProblems
Computational Complexity
Demaine, Fekete, Lang’10: To decide if a set of circles can be
packed into a square is NP-hard.
Approximation Algorithms:
(cid:73) Efficient Algorithms (polynomial time)
(cid:73) Analysis: How far from the optimum solution value ?
(cid:73) Compromise:
Computational Time × Solution Quality
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