Covering polygons with minimum number of rectangles

Christos levcopoulos
  • Andrzej Lingas
Contibuted Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 166)


In the fabrication of masks for integrated circuits, it is desirable to replace the polygons comprising the layout of a circuit with as small as possible number of rectangles. Let Q be the set of all simple polygons with interior angles ≥ 90 degrees. Given a polygon P ε Q, let ϑ(P) be the minimum number of (possibly overlapping) rectangles lying within P necessary to cover P, and let r(P) be the ratio between the length of the longest edge of P and the length of the shortest edge of P. For every natural n ≥ 5, and k, a uniform polygon P n,k with n corners is constructed such that r(P n,k ) ≥ k and ϑ(P n ) ≥ ω(nloglog(r(P n,k ))). On the other hand, by modifying a known heuristic it is shown that for all convex polygons P in Q with n vertices ϑ(P) ≤ O(nlog(r(P))).


Equilateral Triangle Convex Polygon Simple Polygon Interior Angle Short Edge 
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  1. [1]
    Chaiken, S., D.J. Kleitman, M. Saks and J. Shearer, Covering regions by rectangles, SIAM J. Alg. Disc. Meth., vol. 2, no. 4, 1981.Google Scholar
  2. [2]
    Hegedus, A., Algorithms for covering polygons by rectangles, Computer Aided Design, vol. 14, no. 5, 1982.Google Scholar
  3. [3]
    Levcopoulos, C., On Covering Regions with Minimum Number of Rectangles, dissertation in preparation, 1984.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Andrzej Lingas
    • 1
  1. 1.The Department of Computer and Information ScienceLinköping UniversityLinköpingSweden

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