Voronoi Diagrams of Rigidly Moving Sets of Points

Abstract Consider k sets each consisting of n points in the plane, with each set allowed to move rigidly according to some continuous function of time. A paper by Aonuma, Imai, Imai, and Tokuyama shows an upper bound of O(n 3 k 4 log ∗ n) on the number of combinatorial changes to the Voronoi diagram of the kn points over all time. We present a bound of O ( n 2 k 2 λ s ( k )) for s fixed s , thus improving their result by slightly more than a factor of kn .