Making data structures persistent
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
An optimal algorithm for approximate nearest neighbor searching fixed dimensions
Journal of the ACM (JACM)
Kinetic data structures: a state of the art report
WAFR '98 Proceedings of the third workshop on the algorithmic foundations of robotics on Robotics : the algorithmic perspective: the algorithmic perspective
Approximate nearest neighbor queries in fixed dimensions
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Computational Geometry: Theory and Applications
Balanced aspect ratio trees: combining the advantages of k-d trees and octrees
Journal of Algorithms
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
High Dimensional Similarity Search With Space Filling Curves
Proceedings of the 17th International Conference on Data Engineering
Parallel Construction of Quadtrees and Quality Triangulations
WADS '93 Proceedings of the Third Workshop on Algorithms and Data Structures
A Replacement for Voronoi Diagrams of Near Linear Size
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
The skip quadtree: a simple dynamic data structure for multidimensional data
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
ACM Transactions on Algorithms (TALG)
Space-efficient dynamic orthogonal point location, segment intersection, and range reporting
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Optimal dynamic vertical ray shooting in rectilinear planar subdivisions
ACM Transactions on Algorithms (TALG)
A dynamic data structure for approximate range searching
Proceedings of the twenty-sixth annual symposium on Computational geometry
Cloning Voronoi diagrams via retroactive data structures
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
A unified approach to approximate proximity searching
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
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We describe fully retroactive dynamic data structures for approximate range reporting and approximate nearest neighbor reporting. We show how to maintain, for any positive constant d, a set of n points in ℝd indexed by time such that we can perform insertions or deletions at any point in the timeline in O(logn) amortized time. We support, for any small constant ε0, (1+ε)-approximate range reporting queries at any point in the timeline in O(logn+k) time, where k is the output size. We also show how to answer (1+ε)-approximate nearest neighbor queries for any point in the past or present in O(logn) time.