Chips on wafers, or packing rectangles into grids

  • Authors:

  • Mattias Andersson;Joachim Gudmundsson;Christos Levcopoulos

  • Affiliations:

  • Department of Computer Science, Lund University, Box 118, 221 00 Lund, Sweden;Department of Mathematics and Computing Science, TU Eindhoven, 5600 MB Eindhoven, The Netherlands;Department of Computer Science, Lund University, Box 118, 221 00 Lund, Sweden

  • Venue:
  • Computational Geometry: Theory and Applications - Special issue on the 19th European workshop on computational geometry - EuroCG 03
  • Year:
  • 2005

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Abstract

A set of rectangles 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 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 constant @?0 produces a grid packing of S whose area is at most (1+@?) times larger than an optimal grid packing in polynomial time. If @? 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=