Computational geometry: an introduction
Computational geometry: an introduction
A linear-time algorithm for computing the Voronoi diagram of a convex polygon
Discrete & Computational Geometry
Journal of Algorithms
Off-line dynamic maintenance of the width of a planar point set
Computational Geometry: Theory and Applications
Average case analysis of dynamic geometric optimization
Computational Geometry: Theory and Applications
New techniques for some dynamic closest-point and farthest-point problems
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Incremental and decremental maintenance of planar width
Journal of Algorithms
Dynamic planar convex hull operations in near-logarithmic amortized time
Journal of the ACM (JACM)
Dynamic subgraph connectivity with geometric applications
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Semi-online maintenance of geometric optima and measures
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
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We show how to maintain the width of a set of $n$ planar points subjec t to insertions and deletions of points in $O(\sqrt{n}\log^3n)$ amortized time per update. Previously, no fully dynamic algorithm with a guaranteed sublinear time bound was known.