In this paper, we consider the dynamic Voronoi diagram problem. In this problem, a given set of planar points are moving and our objective is to find the Voronoi diagram of these moving points at any time t. A preprocessing algorithm and a query processing algorithm are presented in this paper. Assume that the points are in k-motion, and it takes O(k) time to find the roots of a polynomial with degree O(k). The preprocessing algorithm uses O(k2n3logn•2O(α(n)5k+1)) time to process moving functions of given points, and uses O(k2n3•2O(α(n)5k+1)) space to store the preprocessing result where α(n) is the functional inverse of Ackermann’s function. The query processing algorithm is designed to report the Voronoi diagram of these points for a query time t. It takes O(n) time which is optimal.
CITATION STYLE
Fu, J. J., & Lee, R. C. T. (1990). Voronoi diagrams of moving points in the plane. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 472 LNCS, pp. 238–254). Springer Verlag. https://doi.org/10.1007/3-540-53487-3_49
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