Chips on wafers, or packing rectangles into grids
Author
Summary, in English
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.
Department/s
- Computer Science
Publishing year
2005
Language
English
Pages
95-111
Publication/Series
Computational Geometry
Volume
30
Issue
2
Document type
Journal article
Publisher
Elsevier
Topic
- Computer Science
Keywords
- computational geometry
- approximation algorithms
- packing rectangles
Status
Published
Project
- VR 2002-4049
ISBN/ISSN/Other
- ISSN: 0925-7721