Approximation algorithms for cutting a convex polyhedron out of a sphere

Authors:
Xuehou Tan;Gangshan Wu
Affiliations:
School of Information Science and Technology, Tokai University, 4-1-1 Kitakaname, Hiratsuka 259-1292, Japan;State Key Lab. for Novel Software Technology, Nanjing University, Hankou Road 22, Nanjing 210093, China
Venue:
Theoretical Computer Science
Year:
2013

Citing 8
Cited 0

Finding small simple cycle separators for 2-connected planar graphs

Journal of Computer and System Sciences
Planar Separators

SIAM Journal on Discrete Mathematics
The complexity of cutting paper (extended abstract)

SCG '85 Proceedings of the first annual symposium on Computational geometry
Sets of lines and cutting out polyhedral objects

Computational Geometry: Theory and Applications - Special issue: The European workshop on computational geometry -- CG01
An approximation algorithm for cutting out convex polygons

Computational Geometry: Theory and Applications
A PTAS for Cutting Out Polygons with Lines

Algorithmica
Cutting a Convex Polyhedron Out of a Sphere

Graphs and Combinatorics - The Japan Conference on Computational Geometry and Graphs (JCCGG2009)
Approximation algorithms for cutting out polygons with lines and rays

COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics

Quantified Score

Hi-index	5.23

Visualization

Abstract

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(nlogn) time O(log^2n)-factor approximation, an O(n^1^.^5logn) 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(log^2n)-factor approximation solution.