A PTAS for Cutting Out Polygons with Lines

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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.