问题
I'm looking for an algorithm or data structure to solve the following problem: You are given a set of points S. And you are given Q queries in form of another point. For every query, find the farthest point in the set from the given point.
There are at most 10^5 points in the set and 10^5 queries. All the coordinates for points are in range from 0 to 10^5.
I am wondering if there is a way to store the set of points such that we can answer the queries in O(log n) or O(log^2 n) if necessary.
回答1:
A quote from "Approximate Furthest Neighbor with Application to Annulus Query":
In two dimensions the furthest neighbor problem can be solved in linear space and logarithmic query time using point location in a furthest point Voronoi diagram (see, for example, de Berg et al. [5]).
where [5] refers to the "Marks textbook":
Berg, Mark de, Otfried Cheong, Marc van Kreveld, and Mark Overmars. Computational geometry: algorithms and applications. Springer-Verlag TELOS, 2008.
Farthest-Neighbor Voronoi diagram for a set of eight points.
Image from Jacometti, Welson. "A Note on Primitives for the Manipulation of General Subdivisions and the Computation of Voronoi Diagrams." (1992).
来源：https://stackoverflow.com/questions/54153637/how-to-find-the-farthest-point-from-a-set-of-points-from-a-given-point-efficie