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
Efficiently Planning Compliant Motion in thePlane
SIAM Journal on Computing
Computing the discrepancy with applications to supersampling patterns
ACM Transactions on Graphics (TOG)
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
Applying Parallel Computation Algorithms in the Design of Serial Algorithms
Journal of the ACM (JACM)
Design of Dynamic Data Structures
Design of Dynamic Data Structures
Reporting Red-Blue Intersections between Two Sets of Connected Line Segments
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
Taking a Walk in a Planar Arrangement
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
A fully dynamic algorithm for planar
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Computing the visibility graph of points within a polygon
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
A dynamic data structure for 3-d convex hulls and 2-d nearest neighbor queries
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
An experimental analysis of self-adjusting computation
Proceedings of the 2006 ACM SIGPLAN conference on Programming language design and implementation
On bounded leg shortest paths problems
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the twenty-fourth annual symposium on Computational geometry
Optimal simplification of polygonal chains for subpixel-accurate rendering
Computational Geometry: Theory and Applications
The projection median of a set of points
Computational Geometry: Theory and Applications
A dynamic data structure for 3-D convex hulls and 2-D nearest neighbor queries
Journal of the ACM (JACM)
Three problems about dynamic convex hulls
Proceedings of the twenty-seventh annual symposium on Computational geometry
k-sets of convex inclusion chains of planar point sets
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
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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(log1+&egr;n) amori tzed time and queries take O (log n time each, where n is the maximum size of P and &egr; is any fixed positive constant. For some advanced queries such as bridge-finding, both our bounds increase to O(log3/2n). The only previous fully dynamic solution was by Overmars and van Leeuwen from 1981 and required O(log2n) time per update and O(log n) time per query.