Data structures and algorithms 3: multi-dimensional searching and computational geometry
Data structures and algorithms 3: multi-dimensional searching and computational geometry
Computational geometry: an introduction
Computational geometry: an introduction
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
An improved algorithm for constructing kth-order voronoi diagrams
IEEE Transactions on Computers
Introduction to algorithms
Journal of Algorithms
Randomized multidimensional search trees: lazy balancing and dynamic shuffling (extended abstract)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Dynamic maintenance of geometric structures made easy
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Efficiently Planning Compliant Motion in thePlane
SIAM Journal on Computing
Maintenance of the set of segments visible from a moving viewpoint in two dimensions
Proceedings of the twelfth annual symposium on Computational geometry
Off-line maintenance of planar configurations
Journal of Algorithms
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Constructing Levels in Arrangements and Higher Order Voronoi Diagrams
SIAM Journal on Computing
On range reporting, ray shooting and k-level construction
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Reporting Red-Blue Intersections between Two Sets of Connected Line Segments
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
Random Sampling, Halfspace Range Reporting, and Construction of (= k)-Levels in Three Dimensions
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Approximation algorithms for layered manufacturing
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Online point location in planar arrangements and its applications
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Faster kinetic heaps and their use in broadcast scheduling
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Notes on computing peaks in k-levels and parametric spanning trees
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
ACM SIGACT News
Dynamic Planar Convex Hull with Optimal Query Time
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
Tight degree bounds for pseudo-triangulations of points
Computational Geometry: Theory and Applications - Special issue: The European workshop on computational geometry -- CG01
Taking a Walk in a Planar Arrangement
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Tight bounds for dynamic convex hull queries (again)
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
An experimental analysis of self-adjusting computation
ACM Transactions on Programming Languages and Systems (TOPLAS)
Self-adjusting computation with Delta ML
AFP'08 Proceedings of the 6th international conference on Advanced functional programming
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We give a data structure that allows arbitrary insertions and deletions on a planar point set P and supports basic queries on the convex hull of P, such as membership and tangent-finding. Updates take O(log{1+eps}n) amortized time and queries take O(log n) time each, where n is the maximum size of P and eps is any fixed positive constant. For some advanced queries such as bridge-finding, both our bounds increase to O(log{3/2}n). The only previous fully dynamic solution was by Overmars and van Leeuwen from 1981 and required O(log2 n) time per update.