Dynamic Voronoi diagrams

A new dynamizing technique is introduced whereby n point Voronoi diagrams (both closest and farthest point) can be updated in O(n) time per insertion or deletion, in the worst case. General properties of these dynamic Voronoi diagrams are explored including a storage/ deletion-time trade-off. In addition, their application to such problems as nearest neighbor search and the 2-minimum spanning circle problem is discussed.

[1]  Bruce W. Weide,et al.  Optimal Expected-Time Algorithms for Closest Point Problems , 1980, TOMS.

[2]  D. Matula,et al.  Properties of Gabriel Graphs Relevant to Geographic Variation Research and the Clustering of Points in the Plane , 2010 .

[3]  Jan van Leeuwen,et al.  Dynamization of Decomposable Searching Problems , 1980, Inf. Process. Lett..

[4]  Michael Ian Shamos,et al.  Closest-point problems , 1975, 16th Annual Symposium on Foundations of Computer Science (sfcs 1975).

[5]  Jon Louis Bentley,et al.  Transforming static data structures to dynamic structures , 1979, 20th Annual Symposium on Foundations of Computer Science (sfcs 1979).

[6]  David G. Kirkpatrick,et al.  Optimal Search in Planar Subdivisions , 1983, SIAM J. Comput..

[7]  Godfried T. Toussaint,et al.  PATTERN RECOGNITION AND GEOMETRICAL COMPLEXITY. , 1980 .

[8]  Jon Louis Bentley,et al.  Decomposable Searching Problems , 1979, Inf. Process. Lett..

[9]  Mark H. Overmars,et al.  Dynamization of Order Decomposable Set Problems , 1981, J. Algorithms.

[10]  Edward M. Reingold,et al.  Binary Search Trees of Bounded Balance , 1973, SIAM J. Comput..

[11]  Jan van Leeuwen,et al.  Worst-Case Optimal Insertion and Deletion Methods for Decomposable Searching Problems , 1981, Inf. Process. Lett..

[12]  Robert E. Tarjan,et al.  Finding Minimum Spanning Trees , 1976, SIAM J. Comput..

[13]  D. T. Lee,et al.  Two-Dimensional Voronoi Diagrams in the Lp-Metric , 1980, J. ACM.

[14]  Robert E. Tarjan,et al.  Applications of a planar separator theorem , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).

[15]  David G. Kirkpatrick,et al.  Efficient computation of continuous skeletons , 1979, 20th Annual Symposium on Foundations of Computer Science (sfcs 1979).