Chips on Wafers

(Extended Abstract)
  • Mattias Andersson
  • Joachim Gudmundsson
  • Christos Levcopoulos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2748)


A set of rectangles \(\mathcal{S}\) is said to be grid packed 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 \(\mathcal{S}\) 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 \(\mathcal{S}\) of rectangles and a real constant ε> 0 produces a grid packing of \(\mathcal{S}\) whose area is at most (1 + ε) times larger than an optimal packing in polynomial time. If ε 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 ≤ n rectangles, and given a region \(\mathcal{A}\) grid pack as many rectangles as possible within \(\mathcal{A}\). Apart from the approximation algorithms we present several hardness results.


Approximation Algorithm Directed Edge Rectangular Region Weight Class Optimal Packing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Mattias Andersson
    • 1
  • Joachim Gudmundsson
    • 2
  • Christos Levcopoulos
    • 1
  1. 1.Department of Computer ScienceLund UniversityLundSweden
  2. 2.Department of Mathematics and Computing ScienceTU EindhovenEindhovenThe Netherlands

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