Approximate Voronoi Diagrams of Moving Points

Abstract

We present a new type of Approximate Voronoi Diagrams (AVD) for sets of points in R^d. It has the advantage that it can be maintained efficiently for a set of moving points in R^d, as opposed to previous approaches based on quadtrees. In fixed dimension d, for a set of n points moving at constant velocity, with spread Φ, and for a relative error bound ε, we can maintain our AVD in overall O(n^3 log^2(Φ)/ε^(d^2+d)) time. We also present a simpler construction for approximate Point Location among Equal Balls (PLEB), which can be maintained efficiently for a set of moving points.