Efficient Dynamic Approximate Distance Oracles for Vertex-Labeled Planar Graphs - Laish, Itay; Mozes, Shay (Theory of computing systems, 2019)
Let G be a graph where each vertex is associated with a label. A vertex-labeled approximate distance oracle is a data structure that, given a vertex v and a label λ , returns a (1 + ε )-approximation of the distance from v to the closest vertex with label λ in G . Such an oracle is dynamic if it also supports label changes. In this paper we present three different dynamic approximate vertex-labeled distance oracles for planar graphs, all with polylogarithmic query and update times, and nearly linear space requirements. No such oracles were previously known.