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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 \(\lambda \), returns a \((1+\varepsilon )\)-approximation of the distance from v to the closest vertex with label \(\lambda \) 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.

Efficient Dynamic Approximate Distance Oracles for Vertex-Labeled Planar Graphs