Approximation algorithms for cutting a convex polyhedron out of a sphere

Authors:
Xuehou Tan;Gangshan Wu
Affiliations:
Tokai University, Hiratsuka, Japan;State Key Lab. for Novel Software Technology, Nanjing University, Nanjing, China
Venue:
FAW-AAIM'11 Proceedings of the 5th joint international frontiers in algorithmics, and 7th international conference on Algorithmic aspects in information and management
Year:
2011

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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 log n) time O(log2 n)-factor approximation, an O(n1.5 log n) time O(log n)-factor approximation, and an O(1)-factor approximation with exponential running time. Our results significantly improve upon the previous O(n3) time O(log2 n)-factor approximation solution.