A linear-time heuristic for minimum rectangular coverings (Extended abstract)

  • Christos Levcopoulos
  • Joachim Gudmundsson
Technical Contributions
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1279)


We consider the problem of covering polygons, without any acute interior angles, with rectangles. The rectangles must lie entirely within the polygon and it is preferable to cover the polygon with as few rectangles as possible. Let P be an arbitrary hole-free input polygon, with n vertices, coverable by rectangles. Let μ(P) denote the minimum number of rectangles required to cover P. In this paper we show, by using new techniques, that it is possible to construct a covering within an O(α(n)) approximation factor in O(n+μ(P)) time, where α(n) is the extremely slowly growing inverse of Ackermann's function. This improves the Ω(n0.49...) worst-case approximation factor in time O(n log n+μ(P)) known before.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Christos Levcopoulos
    • 1
  • Joachim Gudmundsson
    • 1
  1. 1.Department of Computer ScienceLund UniversityLundSweden

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