Computational geometry: an introduction
Computational geometry: an introduction
Multidimensional data structures: review and outlook
Advances in computers
The design and analysis of spatial data structures
The design and analysis of spatial data structures
On the complexity of computing the measure of ∪[ai,bi]
Communications of the ACM
New upper bounds in Klee's measure problem
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
An improved algorithm for computing the volume of the union of cubes
Proceedings of the twenty-sixth annual symposium on Computational geometry
Rectangle-efficient aggregation in spatial data streams
PODS '12 Proceedings of the 31st symposium on Principles of Database Systems
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The Klee's measure problem is to compute the volume of the union of a given set of n isothetic boxes in a d-dimensional space. The fastest currently known algorithm for this problem, developed by Over-mars and Yap [6], runs in time O(nd/2 log n). We present an alternative simple approach with the same asymptotic performance. The exposition is restricted to dimensions three and four.