Approximating the volume of unions and intersections of high-dimensional geometric objects
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Publication:982950
DOI10.1016/j.comgeo.2010.03.004zbMath1206.65072OpenAlexW3122481131MaRDI QIDQ982950
Karl Bringmann, Tobias Friedrich
Publication date: 28 July 2010
Published in: Computational Geometry (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.comgeo.2010.03.004
volumealgorithmpolytopesapproximationspheresmeasureconvex bodiesboxesKlee's measure problemintersection of geometric objectsunion of geometric objects
Computational aspects related to convexity (52B55) Numerical aspects of computer graphics, image analysis, and computational geometry (65D18)
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Cites Work
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- A (slightly) faster algorithm for Klee's measure problem
- Computing the volume is difficult
- Simulated annealing in convex bodies and an \(O^{*}(n^{4}\)) volume algorithm
- On the hardness of approximate reasoning
- Counting independent sets up to the tree threshold
- The problem of calculating the volume of a polyhedron is enumerably hard
- A note on a method for generating points uniformly on n -dimensional spheres
- Can the Measure of ∪ n 1 [ a i , b i be Computed in Less Than O(n logn) Steps?]
- Counting without sampling
- Approximating the Volume of Unions and Intersections of High-Dimensional Geometric Objects
- On the Complexity of Computing the Volume of a Polyhedron
- Monte-Carlo approximation algorithms for enumeration problems
- The measure problem for rectangular ranges in d-space
- New Upper Bounds in Klee’s Measure Problem
- On the complexity of computing the measure of ∪[a i ,b i ]
- Random walks in a convex body and an improved volume algorithm
- A random polynomial-time algorithm for approximating the volume of convex bodies
- Random walks and anO*(n5) volume algorithm for convex bodies
- Semi-Online Maintenance of Geometric Optima and Measures
- Thin Partitions: Isoperimetric Inequalities and Sampling Algorithms for some Nonconvex Families