New upper bounds in Klee's measure problem
SIAM Journal on Computing
On the complexity of computing the measure of ∪[ai,bi]
Communications of the ACM
Inclusion-exclusion formulas from independent complexes
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
A (slightly) faster algorithm for klee's measure problem
Proceedings of the twenty-fourth annual symposium on Computational geometry
A (slightly) faster algorithm for Klee's measure problem
Computational Geometry: Theory and Applications
Approximating the volume of unions and intersections of high-dimensional geometric objects
Computational Geometry: Theory and Applications
Klee's measure problem on fat boxes in time ∂(n(d+2)/3)
Proceedings of the twenty-sixth annual symposium on Computational geometry
An improved algorithm for computing the volume of the union of cubes
Proceedings of the twenty-sixth annual symposium on Computational geometry
Computing toolpaths for 5-axis NC machines
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part I
The union of probabilistic boxes: maintaining the volume
ESA'11 Proceedings of the 19th European conference on Algorithms
The mono- and bichromatic empty rectangle and square problems in all dimensions
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
An improved algorithm for Klee's measure problem on fat boxes
Computational Geometry: Theory and Applications
On Klee's measure problem for grounded boxes
Proceedings of the twenty-eighth annual symposium on Computational geometry
Computing feasible toolpaths for 5-axis machines
Theoretical Computer Science
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Let C be a set of n axis-aligned cubes in R3, and let U(C) denote the union of C. We present an algorithmthat can compute the volume of U(C) in time O(n4/3 log n). The previously best known algorithm, by Overmars and Yap, computes the volume of the union ofany n axis-aligned boxes in R3 in O(n3/2log n) time.