A PTAS for cutting out polygons with lines

Authors:
Sergey Bereg;Ovidiu Daescu;Minghui Jiang
Affiliations:
Department of Computer Science, University of Texas at Dallas, Richardson, Texas;Department of Computer Science, University of Texas at Dallas, Richardson, Texas;Department of Computer Science, Utah State University, Logan, Utah
Venue:
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
Year:
2006

Citing 6
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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.