A PTAS for Cutting Out Polygons with Lines

  • Sergey Bereg
  • Ovidiu Daescu
  • Minghui Jiang
Conference paper

DOI: 10.1007/11809678_20

Part of the Lecture Notes in Computer Science book series (LNCS, volume 4112)
Cite this paper as:
Bereg S., Daescu O., Jiang M. (2006) A PTAS for Cutting Out Polygons with Lines. In: Chen D.Z., Lee D.T. (eds) Computing and Combinatorics. COCOON 2006. Lecture Notes in Computer Science, vol 4112. Springer, Berlin, Heidelberg

Abstract

We present a simple O(m + n6/ε12) time (1+ε)-approximation algorithm for the problem of cutting a convex n-gon out of a convex m-gon with line cuts of minimum total cutting length. This problem was introduced by Overmars and Welzl in the First Annual ACM Symposium on Computational Geometry in 1985. We also present a constant approximation algorithm for the generalized problem of cutting two disjoint convex polygons out of a convex polygon.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Sergey Bereg
    • 1
  • Ovidiu Daescu
    • 1
  • Minghui Jiang
    • 2
  1. 1.Department of Computer ScienceUniversity of Texas at DallasRichardsonUSA
  2. 2.Department of Computer ScienceUtah State UniversityLoganUSA

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