Abstract

We present a general technique for approximating various descriptors of the extent of a set P of n points in R . For a given extent measure and a parameter " > 0, it computes in time O(n + 1=" ) a subset Q P of size 1=" , with the property that (1 ")(P ) (Q) (P ). The speci c applications of our technique include "-approximation algorithms for (i) computing diameter, width, and smallest bounding box, ball, and cylinder of P , (ii) maintaining all the previous measures for a set of moving points, and (iii) tting spheres and cylinders through a point set P . Our algorithms are considerably simpler, and faster in many cases, than the known algorithms.

Citations