An optimal-time algorithm for slope selection
SIAM Journal on Computing
Discrete & Computational Geometry - Selected papers from the fifth annual ACM symposium on computational geometry, Saarbrücken, Germany, June 5-11, 1989
Temporal conditions and integrity constraints in active database systems
SIGMOD '95 Proceedings of the 1995 ACM SIGMOD international conference on Management of data
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
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
PODS '99 Proceedings of the eighteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Data structures for mobile data
Journal of Algorithms
Updating and Querying Databases that Track Mobile Units
Distributed and Parallel Databases - Special issue on mobile data management and applications
Indexing moving points (extended abstract)
PODS '00 Proceedings of the nineteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Indexing the positions of continuously moving objects
SIGMOD '00 Proceedings of the 2000 ACM SIGMOD international conference on Management of data
A foundation for representing and querying moving objects
ACM Transactions on Database Systems (TODS)
Multidimensional binary search trees used for associative searching
Communications of the ACM
Design of Dynamic Data Structures
Design of Dynamic Data Structures
Modeling and Querying Moving Objects
ICDE '97 Proceedings of the Thirteenth International Conference on Data Engineering
Novel Approaches in Query Processing for Moving Object Trajectories
VLDB '00 Proceedings of the 26th International Conference on Very Large Data Bases
Analysis of KDT-Trees: KD-Trees Improved by Local Reogranisations
WADS '89 Proceedings of the Workshop on Algorithms and Data Structures
Time Responsive External Data Structures for Moving Points
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
STAR-Tree: An Efficient Self-Adjusting Index for Moving Objects
ALENEX '02 Revised Papers from the 4th International Workshop on Algorithm Engineering and Experiments
Reporting Red-Blue Intersections between Two Sets of Connected Line Segments
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
Improved bounds on planar k-sets and k-levels
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Smooth kinetic maintenance of clusters
Proceedings of the nineteenth annual symposium on Computational geometry
Kinetic sorting and kinetic convex hulls
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Smooth kinetic maintenance of clusters
Computational Geometry: Theory and Applications - Special issue on the 19th annual symposium on computational geometry - SoCG 2003
Competitive algorithms for maintaining a mobile center
Mobile Networks and Applications
Kinetic and dynamic data structures for convex hulls and upper envelopes
Computational Geometry: Theory and Applications
Kinetic sorting and kinetic convex hulls
Computational Geometry: Theory and Applications
Kinetic KD-trees and longest-side KD-trees
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Out-of-order event processing in kinetic data structures
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Kinetic and dynamic data structures for closest pair and all nearest neighbors
ACM Transactions on Algorithms (TALG)
The projection median of a set of points
Computational Geometry: Theory and Applications
Smooth kinetic maintenance of clusters
Computational Geometry: Theory and Applications - Special issue on the 19th annual symposium on computational geometry - SoCG 2003
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Kinetic kd-Trees and Longest-Side kd-Trees
SIAM Journal on Computing
Median trajectories using well-visited regions and shortest paths
Proceedings of the 19th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
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We propose algorithms for maintaining two variants of kd- trees of a set of moving points in the plane. A pseudo kd-tree allows the number of points stored in the two children to differ by a constant factor. An overlapping kd-tree allows the bounding boxes of two children to overlap. We show that both of them support range search operations in O(n1/2+驴) time, where 驴 only depends on the approximation precision. As the points move, we use event-based kinetic data structures to update the tree when necessary. Both trees undergo only a quadratic number of events, which is optimal, and the update cost for each event is only poly-logarithmic. To maintain the pseudo kd-tree, we develop algorithms for computing an approximate median level of a line arrangement, which itself is of great interest. We show that the computation of the approximate median level of a set of lines or line segments can be done in an online fashion smoothly, i.e., there are no expensive updates for any events. For practical consideration, we study the case in which there are speed-limit restrictions or smooth trajectory requirements. The maintenance of the pseudo kd-tree, as a consequence of the approximate median algorithm, can also adapt to those restrictions.