We show that for any set of n points moving along "simple" trajectories
(i.e., each coordinate is described with a polynomial of bounded degree) in
ℜd and any parameter 2≤k≤n, one can select a fixed non-empty
subset of the points of size O(klogk), such that the Voronoi diagram of
this subset is "balanced" at any given time (i.e., it contains O(n/k) points
per cell). We also show that the bound O(klogk) is near optimal even for
the one dimensional case in which points move linearly in time. As
applications, we show that one can assign communication radii to the sensors of
a network of n moving sensors so that at any given time their interference is
O(nlogn). We also show some results in kinetic approximate range
counting and kinetic discrepancy. In order to obtain these results, we extend
well-known results from ε-net theory to kinetic environments