Abstract
This paper studies the problem of cutting out a given polygon, drawn on a convex piece of paper, in the cheapest possible way. For the problems of cutting out convex polygons with line cuts and ray cuts, we present a 7.9-approximation algorithm and a 6-approximation algorithm, respectively. For the problem of cutting out ray-cuttable polygons, an O(log n)-approximation algorithm is given.
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References
Bhadury, J., Chandrasekaran, R.: Stock cutting to minimize cutting sequence. European Journal of Operational Research 88, 69–87 (1996)
Daescu, O., Luo, J.: Cutting out polygons with lines and rays. In: Fleischer, R., Trippen, G. (eds.) ISAAC 2004. LNCS, vol. 3341, pp. 669–680. Springer, Heidelberg (2004)
Demaine, E.D., Demaine, M.L., Kaplan, C.S.: Polygons cuttable by a circular saw. Computational Geometry: Theory and Applications 20, 69–84 (2001)
Dumitrescu, A.: An approximation algorithm for cuttng out convex polygons. Computational Geometry: Theory and Applications 29, 223–231 (2004)
Overmars, M.H., Welzl, E.: The complexity of cutting paper. In: Proc. of the 1st Annual ACM Symposium on Computational Geometry, pp. 316–321 (1985)
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Tan, X. (2005). Approximation Algorithms for Cutting Out Polygons with Lines and Rays. In: Wang, L. (eds) Computing and Combinatorics. COCOON 2005. Lecture Notes in Computer Science, vol 3595. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11533719_54
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DOI: https://doi.org/10.1007/11533719_54
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28061-3
Online ISBN: 978-3-540-31806-4
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