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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.
Gowda et al. (Thu,) studied this question.