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
Discrete & Computational Geometry - Selected papers from the fifth annual ACM symposium on computational geometry, Saarbrücken, Germany, June 5-11, 1989
Maintenance of geometric extrema ∈
Journal of the ACM (JACM)
Dynamic maintenance of geometric structures made easy
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Journal of Algorithms
Fully dynamic Delaunay triangulation in logarithmic expected time per operation
Computational Geometry: Theory and Applications
Reporting points in halfspaces
Computational Geometry: Theory and Applications
Four results on randomized incremental constructions
Computational Geometry: Theory and Applications
Deterministic algorithms for 2-D convex programming and 3-D Online linear programming
Journal of Algorithms
On range reporting, ray shooting and k-level construction
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Fast hierarchical clustering and other applications of dynamic closest pairs
Journal of Experimental Algorithmics (JEA)
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)
Taking a Walk in a Planar Arrangement
SIAM Journal on Computing
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Semi-Online Maintenance of Geometric Optima and Measures
SIAM Journal on Computing
Low-Dimensional Linear Programming with Violations
SIAM Journal on Computing
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Optimal halfspace range reporting in three dimensions
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Optimal cover of points by disks in a simple polygon
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
FIFO indexes for decomposable problems
Proceedings of the thirtieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Minimizing the error of linear separators on linearly inseparable data
Discrete Applied Mathematics
Bounded-degree polyhedronization of point sets
Computational Geometry: Theory and Applications
Unions of onions: preprocessing imprecise points for fast onion layer decomposition
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
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We present a fully dynamic randomized data structure that can answer queries about the convex hull of a set of n points in three dimensions, where insertions take O(log3n) expected amortized time, deletions take O(log6n) expected amortized time, and extreme-point queries take O(log2n) worst-case time. This is the first method that guarantees polylogarithmic update and query cost for arbitrary sequences of insertions and deletions, and improves the previous O(n&epsis;)-time method by Agarwal and Matoušek a decade ago. As a consequence, we obtain similar results for nearest neighbor queries in two dimensions and improved results for numerous fundamental geometric problems (such as levels in three dimensions and dynamic Euclidean minimum spanning trees in the plane).