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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$\Re^d$ and any parameter $2 \le k \le n$, one can select a fixed non-emptysubset of the points of size $O(k \log k)$, such that the Voronoi diagram ofthis subset is "balanced" at any given time (i.e., it contains $O(n/k)$ pointsper cell). We also show that the bound $O(k \log k)$ is near optimal even forthe one dimensional case in which points move linearly in time. Asapplications, we show that one can assign communication radii to the sensors ofa network of $n$ moving sensors so that at any given time their interference is$O(\sqrt{n\log n})$. We also show some results in kinetic approximate rangecounting and kinetic discrepancy. In order to obtain these results, we extendwell-known results from $\varepsilon$-net theory to kinetic environments.

On interference among moving sensors and related problems