, Volume 53, Issue 2, pp 157–171

A PTAS for Cutting Out Polygons with Lines



We present a simple O(m+n6/ε12) time (1+ε)-approximation algorithm for finding a minimum-cost sequence of lines to cut a convex n-gon out of a convex m-gon.


Approximation algorithms Stock cutting 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bhadury, J., Chandrasekaran, R.: Stock cutting to minimize cutting length. Eur. J. Oper. Res. 88, 69–87 (1996) MATHCrossRefGoogle Scholar
  2. 2.
    Chandrasekaran, R., Daescu, O., Luo, J.: Cutting out polygons. In: Proceedings of the 17th Canadian Conference on Computational Geometry (CCCG’05), pp. 183–186 (2005) Google Scholar
  3. 3.
    Daescu, O., Luo, J.: Cutting out polygons with lines and rays. Int. J. Comput. Geom. Appl. 16, 227–248 (2006) MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Demaine, E.D., Demaine, M.L., Kaplan, C.S.: Polygons cuttable by a circular saw. Comput. Geom. Theory Appl. 20, 69–84 (2001) MATHMathSciNetGoogle Scholar
  5. 5.
    Dumitrescu, A.: An approximation algorithm for cutting out convex polygons. Comput. Geom. Theory Appl. 29, 223–231 (2004) MATHMathSciNetGoogle Scholar
  6. 6.
    Dumitrescu, A.: The cost of cutting out convex n-gons. Discrete Appl. Math. 143, 353–358 (2004) MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Overmars, M.H., Welzl, E.: The complexity of cutting paper. In: Proceedings of the 1st Annual ACM Symposium on Computational Geometry (SoCG’85), pp. 316–321 (1985) Google Scholar
  8. 8.
    Tan, X.: Approximation algorithms for cutting out polygons with lines and rays. In: Proceedings of the 11th International Computing and Combinatorics Conference (COCOON’05), LNCS 3595, pp. 534–543 (2005) Google Scholar
  9. 9.
    Zwillinger, D.: CRC Standard Mathematical Tables and Formulae, 31st edn. CRC Press, Boca Raton (2002) Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of Texas at DallasRichardsonUSA
  2. 2.Department of Computer ScienceUtah State UniversityLoganUSA

Personalised recommendations