Abstract
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.
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