Revenge of the Dog: Queries on Voronoi Diagrams of Moving Points
نویسندگان
چکیده
Suppose we are given n moving postmen described by their motion equations pi(t) = si + vit; i = 1; : : : ; n, where si 2 IR 2 is the position of the i'th postman at time t = 0, and vi 2 IR 2 is his velocity. The problem we address is how to preprocess the postmen data so as to be able to e ciently answer two types of nearest neighbor queries. The rst one asks \who is the nearest postman at time tq to a dog located at point sq?". In the second type a query dog is located a point sq at time tq, its velocity is vq > jvij (for all i = 1; : : : ; n), and we want to know which postman the dog can catch rst. We present two solutions to these problems, with tradeo between preprocessing time and query time. Both solutions use deterministic data structures. Key-words: Computational geometry, Location structures, Parametric search
منابع مشابه
Queries on Voronoi Diagrams of Moving Points
Suppose we are given n moving postmen described by their motion equations p i (t) = s i + v i t; i = 1; : : : ; n, where s i 2 I R 2 is the position of the i'th postman at time t = 0, and v i 2 I R 2 is his velocity. The problem we address is how to preprocess the postmen data so as to be able to eeciently answer two types of nearest-neighbor queries. The rst one asks who is the nearest postman...
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