Evanthia Papadopoulou: Deletion in abstract Voronoi diagrams in expected linear time

Abstract: Updating an abstract Voronoi diagram in linear time, after deletion of one site, has been an open problem for a long time. Similarly for various concrete Voronoi diagrams of generalized sites, other than points. In this talk I will present a simple, expected linear-time algorithm to update an abstract Voronoi diagram after deletion. To this goal, I will introduce the concept of a Voronoi-like diagram, a relaxed version of a Voronoi construct that has a structure similar to an abstract Voronoi diagram, without however being one. Voronoi-like diagrams serve as intermediate structures, which are considerably simpler to compute, thus, making an expected linear-time construction possible.

Joint work with Kolja Junginger