 
Summary: LinearSize Approximate Voronoi Diagrams
Sunil Arya
Theocharis Malamatos
Abstract
Given a set S of n points in IRd
, a (t, )approximate
Voronoi diagram (AVD) is a partition of space into constant
complexity cells, where each cell c is associated with t
representative points of S, such that for any point in c, one
of the associated representatives approximates the nearest
neighbor to within a factor of (1+). The goal is to minimize
the number and complexity of the cells in the AVD. We show
that it is possible to construct an AVD consisting of O(n/d
)
cells for t = 1, and O(n) cells for t = O(1/(d1)/2
). In
general, for a real parameter 2 1/, we show that
it is possible to construct a (t, )AVD consisting of O(nd
)
cells for t = O(1/()(d1)/2
