Abstract
We present a simple O(m+n 6/ε 12) 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.
Similar content being viewed by others
References
Bhadury, J., Chandrasekaran, R.: Stock cutting to minimize cutting length. Eur. J. Oper. Res. 88, 69–87 (1996)
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)
Daescu, O., Luo, J.: Cutting out polygons with lines and rays. Int. J. Comput. Geom. Appl. 16, 227–248 (2006)
Demaine, E.D., Demaine, M.L., Kaplan, C.S.: Polygons cuttable by a circular saw. Comput. Geom. Theory Appl. 20, 69–84 (2001)
Dumitrescu, A.: An approximation algorithm for cutting out convex polygons. Comput. Geom. Theory Appl. 29, 223–231 (2004)
Dumitrescu, A.: The cost of cutting out convex n-gons. Discrete Appl. Math. 143, 353–358 (2004)
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)
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)
Zwillinger, D.: CRC Standard Mathematical Tables and Formulae, 31st edn. CRC Press, Boca Raton (2002)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bereg, S., Daescu, O. & Jiang, M. A PTAS for Cutting Out Polygons with Lines. Algorithmica 53, 157–171 (2009). https://doi.org/10.1007/s00453-008-9182-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00453-008-9182-2