3 research outputs found
On interference among moving sensors and related problems
We show that for any set of points moving along "simple" trajectories
(i.e., each coordinate is described with a polynomial of bounded degree) in
and any parameter , one can select a fixed non-empty
subset of the points of size , such that the Voronoi diagram of
this subset is "balanced" at any given time (i.e., it contains points
per cell). We also show that the bound 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 moving sensors so that at any given time their interference is
. 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 -net theory to kinetic environments
On Interference Among Moving Sensors and Related Problems
We show that for any set of n moving points in R^d and any parameter 2<=k<n, one can select a fixed non-empty subset of the points of size O(k log k), 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(k log k) is near optimal even for the one dimensional case in which points move linearly in time. As an application, we show that one can assign communication radii to the sensors of a network of moving sensors so that at any given time, their interference is O( (n log n)^0.5). This is optimal up to an O((log n)^0.5) factor
On interference among moving sensors and related problems
\u3cp\u3eWe show that for any set of n moving points in R\u3csup\u3ed\u3c/sup\u3e and any parameter 2 ≤ k ≤ n, one can select a fixed non-empty subset of the points of size O(k log k), 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(k log k) is near optimal even for the one dimensional case in which points move linearly in time. As an application, 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(√n log n). This is optimal up to an O(√log n) factor.\u3c/p\u3