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A PTAS for Cutting Out Polygons with Lines

  • Sergey Bereg
  • Ovidiu Daescu
  • Minghui Jiang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4112)

Abstract

We present a simple O(m + n 6/ε 12) 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.

Keywords

Computational Geometry Convex Polygon Polygonal Chain Portal Point Cutting Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Bhadury, J., Chandrasekaran, R.: Stock cutting to minimize cutting length. European Journal of Operations Research 88, 69–87 (1996)MATHCrossRefGoogle Scholar
  2. 2.
    Daescu, O., Luo, J.: Cutting out polygons with lines and rays. International Journal of Computational Geometry & Applications, 16(2-3), 227–248 (2006); In: Fleischer, R., Trippen, G. (eds.) ISAAC 2004. LNCS, vol. 3341, pp. 669–680. Springer, Heidelberg (2004) (preliminary version)Google Scholar
  3. 3.
    Demaine, E.D., Demaine, M.L., Kaplan, C.S.: Polygons cuttable by a circular saw. Computational Geometry: Theory and Applications 20, 69–84 (2001)MATHMathSciNetGoogle Scholar
  4. 4.
    Dumitrescu, A.: An approximation algorithm for cutting out convex polygons. Computational Geometry: Theory and Applications 29, 223–231 (2004); In: Proceedings of the 14th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2003), pp. 823–827 (2003) (preliminary version)Google Scholar
  5. 5.
    Dumitrescu, A.: The cost of cutting out convex n-gons. Discrete Applied Mathematics 143(1-3), 353–358 (2004)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Overmars, M.H., Welzl, E.: The complexity of cutting paper. In: Proceedings of the 1st Annual ACM Symposium on Computational Geometry (SoCG 1985), pp. 316–321 (1985)Google Scholar
  7. 7.
    Pachand, J., Tardos, G.: Cutting glass. Discrete Computational Geometry 24, 481–495 (2000)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Tan, X.: Approximation algorithms for cutting out polygons with lines and rays. In: Wang, L. (ed.) COCOON 2005. LNCS, vol. 3595, pp. 534–543. Springer, Heidelberg (2005)CrossRefGoogle Scholar

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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