Stable unmerging in linear time and constant space
Information Processing Letters
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
Communications of the ACM
Asymptotically efficient in-place merging
Theoretical Computer Science
Towards in-place geometric algorithms and data structures
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Space-efficient planar convex hull algorithms
Theoretical Computer Science - Latin American theorotical informatics
Line-segment intersection made in-place
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
Rectangle-efficient aggregation in spatial data streams
PODS '12 Proceedings of the 31st symposium on Principles of Database Systems
An in-place min-max priority search tree
Computational Geometry: Theory and Applications
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We present the first in-place algorithm for solving Klee's measure problem for a set of n axis-parallel rectangles in the plane. Our algorithm runs in O(n^3^/^2logn) time and uses O(1) extra words in addition to the space needed for representing the input. The algorithm is surprisingly simple and thus very likely to yield an implementation that could be of practical interest. As a byproduct, we develop an optimal algorithm for solving Klee's measure problem for a set of n intervals; this algorithm runs in optimal time O(nlogn) and uses O(1) extra space.