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Journal of Combinatorial Optimization

, Volume 3, Issue 4, pp 437–452 | Cite as

Close Approximations of Minimum Rectangular Coverings

  • Joachim Gudmundsson
  • Christos Levcopoulos
Article

Abstract

We consider the problem of covering arbitrary polygons with rectangles. The rectangles must lie entirely within the polygon. (This requires that the interior angles of the polygon are all greater than or equal to 90 degrees.) We want to cover the polygon with as few rectangles as possible. This problem has an application in fabricating masks for integrated circuits.

In this paper we will describe the first polynomial algorithm, guaranteeing an O(log n) approximation factor, provided that the n vertices of the input polygon are given as polynomially bounded integer coordinates. By the same technique we also obtain the first algorithm producing a covering which is within a constant factor of the optimal in exponential time (compared to the doubly-exponential known before).

approximation algorithms computational geometry covering polygons 

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Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

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

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