An approximation algorithm for cutting out convex polygons
نویسندگان
چکیده
منابع مشابه
Cutting Out Polygons
In this paper, we present approximation algorithms for the problem of cutting out a convex polygon P with n vertices from another convex polygon Q with m vertices by a sequence of guillotine cuts of smallest total length. Specifically, we give an O(n + m) running time, constant factor approximation algorithm, and an O(n+m) running time, O(log n)-factor approximation algorithm for cutting P out ...
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We present approximation algorithms for cutting out polygons with line cuts and ray cuts. Our results answer a number of open problems and are either the first solutions or significantly improve over previously known solutions. For the line cutting version, we prove a key property that leads to a simple, constant factor approximation algorithm. For the ray cutting version, we prove it is possib...
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Given a simple (cuttable) polygon Q drawn on a piece of planar material R, we cut Q out of R by a (small) circular saw with a total number of cuts no more than twice the optimal. This improves the previous approximation ratio of 2.5 obtained by Demaine et al. in 2001.
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In tolerancing, the Out-Of-Roundness factor determines the relative circularity of planar shapes. The measurement of concern in this work is the Minimum Radial Separation, as recommended by the American National Standards Institute (ANSI). Here we show that the algorithm given in Le and Lee [6] runs in /9(n 2) time even for convex polygons. Furthermore, we present an optimal O(n) time algorithm...
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For a given convex polyhedron P of n vertices inside a sphere Q , we study the problem of cutting P out of Q by a sequence of plane cuts. The cost of a plane cut is the area of the intersection of the plane with Q , and the objective is to find a cutting sequence that minimizes the total cost. We present three approximation solutions to this problem: an O(n log n) time O(log2 n)-factor approxim...
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 2004
ISSN: 0925-7721
DOI: 10.1016/j.comgeo.2004.01.010