K-d trees for semidynamic point sets
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Deferred data structure for the nearest neighbor problem
Information Processing Letters
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Parallel computational geometry
Parallel computational geometry
On computing Voronoi diagrams by divide-prune-and-conquer
Proceedings of the twelfth annual symposium on Computational geometry
Queries on Voronoi diagrams of moving points
Computational Geometry: Theory and Applications
Parallel processing of nearest neighbor queries in declustered spatial data
GIS '96 Proceedings of the 4th ACM international workshop on Advances in geographic information systems
Implementation and evaluation of an efficient parallel Delaunay triangulation algorithm
Proceedings of the ninth annual ACM symposium on Parallel algorithms and architectures
An Algorithm for Finding Best Matches in Logarithmic Expected Time
ACM Transactions on Mathematical Software (TOMS)
Improving A Solution's Quality Through Parallel Processing
The Journal of Supercomputing
Load Balancing in Parallel Computers: Theory and Practice
Load Balancing in Parallel Computers: Theory and Practice
Scheduling and Load Balancing in Parallel and Distributed Systems
Scheduling and Load Balancing in Parallel and Distributed Systems
Fast Nearest Neighbor Search in High-Dimensional Space
ICDE '98 Proceedings of the Fourteenth International Conference on Data Engineering
A Plane-Sweep Algorithm for the All-Nearest-Neighbors Problem for a Set of Convex Planar Objects
WADS '93 Proceedings of the Third Workshop on Algorithms and Data Structures
Proximity and applications in general metrics
Proximity and applications in general metrics
Efficient parallel processing for K-nearest-neighbor search in spatial databases
ICCSA'06 Proceedings of the 2006 international conference on Computational Science and Its Applications - Volume Part V
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The paper presents the sequential and the parallel algorithm for solving the nearest-neighbor problem in the plane, based on the generalized Voronoi diagram construction. The applications of the problem are found in the areas of networking, communications, distributed systems, computer modeling and information retrieval. The input for the problem is the set of circular sites S with varying radii, the query point p and the metric (Minkowski or power) according to which the site, neighboring the query point, is to be reported. The sequential algorithm takes O(n) time to build the data structure and O(log n) time for each query. The parallel algorithm requires O(log n log) preprocessing time and O(log) query time on EREW PRAM architecture with n/log n processors. The IDG/NNM software was developed for an experimental study of the problem. The experimental results demonstrate that the Voronoi diagram method outperforms the k − d tree method for all tested input configurations. The tests were conducted on large data sets, comprising thousands of generators.