Abstract
This paper presents the following approximation algorithms for computing a minimum cost sequence of planes to cut a convex polyhedron P of n vertices out of a sphere Q: an O(n logn) time O(log2 n)-factor approximation, an O(n 1.5 logn) time O(logn)-factor approximation, and an O(1)-factor approximation with exponential running time. Our results significantly improve upon the previous O(n 3) time O(log2 n)-factor approximation solution.
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Tan, X., Wu, G. (2011). Approximation Algorithms for Cutting a Convex Polyhedron Out of a Sphere. In: Atallah, M., Li, XY., Zhu, B. (eds) Frontiers in Algorithmics and Algorithmic Aspects in Information and Management. Lecture Notes in Computer Science, vol 6681. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21204-8_16
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DOI: https://doi.org/10.1007/978-3-642-21204-8_16
Publisher Name: Springer, Berlin, Heidelberg
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