The graph Voronoi diagram with applications

The Voronoi diagram is a famous structure of computational geometry. We show that there is a straightforward equivalent in graph theory which can be eeciently computed. In particular, we give two algorithms for the computation of graph Voronoi diagrams, prove a lower bound on the problem, and we identify cases where the algorithms presented are optimal. The space requirement of a graph Voronoi diagram is modest, since it needs no more space than the graph itself. The investigation of graph Voronoi diagrams is motivated by many applications and problems on networks that can be easily solved with their help. This includes the computation of nearest facilities, all nearest neighbors and closest pairs, some kind of collision free moving, and anti-centers and closest points.