Chips on wafers, or packing rectangles into grids
Andersson, Mattias LU ; Gudmundsson, J and Levcopoulos, Christos LU
(2005)
In Computational Geometry
30(2).
p.95-111
- Abstract
- A set of rectangles S is said to be gridpacked if there exists a rectangular grid (not necessarily regular) such that every rectangle lies in the grid and there is at most one rectangle of S in each cell. The area of a grid packing is the area of a minimal bounding box that contains all the rectangles in the grid packing. We present an approximation algorithm that given a set S of rectangles and a real epsilon constant epsilon > 0 produces a grid packing of S whose area is at most (1 + epsilon) times larger than an optimal grid packing in polynomial time. If epsilon is chosen large enough the running time of the algorithm will be linear. We also study several interesting variants, for example the smallest area grid packing containing at... (More)
- A set of rectangles S is said to be gridpacked if there exists a rectangular grid (not necessarily regular) such that every rectangle lies in the grid and there is at most one rectangle of S in each cell. The area of a grid packing is the area of a minimal bounding box that contains all the rectangles in the grid packing. We present an approximation algorithm that given a set S of rectangles and a real epsilon constant epsilon > 0 produces a grid packing of S whose area is at most (1 + epsilon) times larger than an optimal grid packing in polynomial time. If epsilon is chosen large enough the running time of the algorithm will be linear. We also study several interesting variants, for example the smallest area grid packing containing at least k less than or equal to n rectangles, and given a region A grid pack as many rectangles as possible within A Apart from the approximation algorithms we present several hardness results. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/258043
- author
- Andersson, Mattias
LU
; Gudmundsson, J
and Levcopoulos, Christos
LU
- organization
- publishing date
- 2005
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- computational geometry, approximation algorithms, packing rectangles
- in
- Computational Geometry
- volume
- 30
- issue
- 2
- pages
- 95 - 111
- publisher
- Elsevier
- external identifiers
-
- wos:000226155000003
- scopus:10044253053
- ISSN
- 0925-7721
- DOI
- 10.1016/j.comgeo.2004.05.006
- project
- VR 2002-4049
- language
- English
- LU publication?
- yes
- id
- d30225b2-e06d-4c2a-b1f6-7c0108824e1b (old id 258043)
- date added to LUP
- 2016-04-01 15:22:12
- date last changed
- 2022-02-05 00:55:13
@article{d30225b2-e06d-4c2a-b1f6-7c0108824e1b,
abstract = {{A set of rectangles S is said to be gridpacked if there exists a rectangular grid (not necessarily regular) such that every rectangle lies in the grid and there is at most one rectangle of S in each cell. The area of a grid packing is the area of a minimal bounding box that contains all the rectangles in the grid packing. We present an approximation algorithm that given a set S of rectangles and a real epsilon constant epsilon > 0 produces a grid packing of S whose area is at most (1 + epsilon) times larger than an optimal grid packing in polynomial time. If epsilon is chosen large enough the running time of the algorithm will be linear. We also study several interesting variants, for example the smallest area grid packing containing at least k less than or equal to n rectangles, and given a region A grid pack as many rectangles as possible within A Apart from the approximation algorithms we present several hardness results.}},
author = {{Andersson, Mattias and Gudmundsson, J and Levcopoulos, Christos}},
issn = {{0925-7721}},
keywords = {{computational geometry; approximation algorithms; packing rectangles}},
language = {{eng}},
number = {{2}},
pages = {{95--111}},
publisher = {{Elsevier}},
series = {{Computational Geometry}},
title = {{Chips on wafers, or packing rectangles into grids}},
url = {{http://dx.doi.org/10.1016/j.comgeo.2004.05.006}},
doi = {{10.1016/j.comgeo.2004.05.006}},
volume = {{30}},
year = {{2005}},
}