Voronoi diagram for multiply-connected polygonal domains 1: algorithm
IBM Journal of Research and Development
An improved algorithm for constructing kth-order voronoi diagrams
IEEE Transactions on Computers
Parallel geometric algorithms on mesh-connected computers
ACM '87 Proceedings of the 1987 Fall Joint Computer Conference on Exploring technology: today and tomorrow
Manhattonian proximity in a simple polygon
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
The Construction of Delaunay Diagrams by Lob Reduction
JCDCG '00 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
Random Geometric Problems on [0, 1]²
RANDOM '98 Proceedings of the Second International Workshop on Randomization and Approximation Techniques in Computer Science
Extreme Distances in Multicolored Point Sets
ICCS '02 Proceedings of the International Conference on Computational Science-Part III
Curve and Surface Reconstruction in R2 and R3
HPC-ASIA '97 Proceedings of the High-Performance Computing on the Information Superhighway, HPC-Asia '97
Relay Node Placement in Wireless Sensor Networks
IEEE Transactions on Computers
Spatial Planning: A Configuration Space Approach
IEEE Transactions on Computers
On k-Nearest Neighbor Voronoi Diagrams in the Plane
IEEE Transactions on Computers
An Optimal Illumination Region Algorithm for Convex Polygons
IEEE Transactions on Computers
Base station placement on boundary of a convex polygon
Journal of Parallel and Distributed Computing
Testing Euclidean minimum spanning trees in the plane
ACM Transactions on Algorithms (TALG)
Fast computation of smallest enclosing circle with center on a query line segment
Information Processing Letters
Kinetic and dynamic data structures for closest pair and all nearest neighbors
ACM Transactions on Algorithms (TALG)
Sensor Network Deployment Using Circle Packings
Information Networking. Towards Ubiquitous Networking and Services
Optimal halfspace range reporting in three dimensions
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
A quasi-polynomial time approximation scheme for minimum weight triangulation
Journal of the ACM (JACM)
Constrained minimum enclosing circle with center on a query line segment
Computational Geometry: Theory and Applications
Divide-and-conquer for Voronoi diagrams revisited
Proceedings of the twenty-fifth annual symposium on Computational geometry
Abstract Voronoi diagrams revisited
Computational Geometry: Theory and Applications
Computing the Implicit Voronoi Diagram in Triple Precision
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Euclidean Voronoi diagram of 3D balls and its computation via tracing edges
Computer-Aided Design
Filtering relocations on a Delaunay triangulation
SGP '09 Proceedings of the Symposium on Geometry Processing
Discovery and selection protocols for multi-hop wireless internet access
International Journal of Computers and Applications
The traveling salesman: computational solutions for TSP applications
The traveling salesman: computational solutions for TSP applications
Efficient and accurate nearest neighbor and closest pair search in high-dimensional space
ACM Transactions on Database Systems (TODS)
Divide-and-conquer for Voronoi diagrams revisited
Computational Geometry: Theory and Applications
IEEE Transactions on Signal Processing
Fast euclidean minimum spanning tree: algorithm, analysis, and applications
Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining
Use of the TRIPOD overlay network for resource discovery
Future Generation Computer Systems
Algorithm engineering: bridging the gap between algorithm theory and practice
Algorithm engineering: bridging the gap between algorithm theory and practice
Randomly projected KD-trees with distance metric learning for image retrieval
MMM'11 Proceedings of the 17th international conference on Advances in multimedia modeling - Volume Part II
Solving the constrained p-center problem using heuristic algorithms
Applied Soft Computing
Constructing two-dimensional Voronoi diagrams via divide-and-conquer of envelopes in space
Transactions on computational science IX
Properties and an approximation algorithm of round-tour Voronoi diagrams
Transactions on computational science IX
Constructing two-dimensional Voronoi diagrams via divide-and-conquer of envelopes in space
Transactions on computational science IX
Properties and an approximation algorithm of round-tour Voronoi diagrams
Transactions on computational science IX
On multiplicatively weighted Voronoi diagrams for lines in the plane
Transactions on computational science XIII
Data-driven trajectory smoothing
Proceedings of the 19th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
SINR diagram with interference cancellation
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
An acceleration technique for the computation of voronoi diagrams using graphics hardware
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and its Applications - Volume Part I
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Constrained minimum enclosing circle with center on a query line segment
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
A spatial cloaking framework based on range search for nearest neighbor search
DPM'09/SETOP'09 Proceedings of the 4th international workshop, and Second international conference on Data Privacy Management and Autonomous Spontaneous Security
Efficient algorithm for placing base stations by avoiding forbidden zone
ICDCIT'05 Proceedings of the Second international conference on Distributed Computing and Internet Technology
Research paper: The saga of minimum spanning trees
Computer Science Review
The weighted euclidean 1-center problem
Operations Research Letters
An O(mn2) algorithm for the Maximin problem in E2
Operations Research Letters
A comment on a minmax location problem
Operations Research Letters
A computational geometry-based local search algorithm for planar location problems
CPAIOR'12 Proceedings of the 9th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Boosting multi-kernel locality-sensitive hashing for scalable image retrieval
SIGIR '12 Proceedings of the 35th international ACM SIGIR conference on Research and development in information retrieval
Convex Distance Functions In 3-Space Are Different
Fundamenta Informaticae
Incremental instant radiosity for real-time indirect illumination
EGSR'07 Proceedings of the 18th Eurographics conference on Rendering Techniques
Fundamenta Informaticae - Emergent Computing
Parallel computing 2D Voronoi diagrams using untransformed sweepcircles
Computer-Aided Design
A navigation mesh for dynamic environments
Computer Animation and Virtual Worlds
Computational Intelligence and Neuroscience
Fast segment insertion and incremental construction of constrained delaunay triangulations
Proceedings of the twenty-ninth annual symposium on Computational geometry
Locating a semi-obnoxious covering facility with repelling polygonal regions
Discrete Applied Mathematics
Fast and robust approximation of smallest enclosing balls in arbitrary dimensions
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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A number of seemingly unrelated problems involving the proximity of N points in the plane are studied, such as finding a Euclidean minimum spanning tree, the smallest circle enclosing the set, k nearest and farthest neighbors, the two closest points, and a proper straight-line triangulation. For most of the problems considered a lower bound of O(N log N) is shown. For all of them the best currently-known upper bound is O(N2) or worse. The purpose of this paper is to introduce a single geometric structure, called the Voronoi diagram, which can be constructed rapidly and contains all of the relevant proximity information in only linear space. The Voronoi diagram is used to obtain O(N log N) algorithms for all of the problems.