Shakhar Smorodinsky

In this paper, we extend the weak 1/r-net theorem to a kinetic setting where the underlying set of points is moving polynomially with bounded description complexity. We establish that one can find a kinetic analog N of a weak 1/r-net of cardinality O(r^d(d+1)/2 log^d r) whose points are moving with coordinates that are rational functions with bounded description complexity. Moreover, each member of N has one polynomial coordinate.