Ready, set, go! the Voronoi diagram of moving points that start from a line

Authors:
Vladlen Koltun
Affiliations:
Computer Science Division, University of California, Berkeley, CA
Venue:
Information Processing Letters
Year:
2004

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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(n2) if the points start their movement from a common line.