Ready, Set, Go! The Voronoi diagram of moving points that start from a line

Abstract

It is an outstanding open problem of computational geometry to prove a near-quadratic upper bound on the number of combinatorial changes in the Voronoi diagram of points moving at a common constant speed along linear trajectories in the plane. In this note we observe that this quantity is Θ( n 2) if the points start their movement from a common line.