Efficient Dynamic Approximate Distance Oracles for Vertex-Labeled Planar Graphs

TL;DR

This paper introduces three efficient dynamic approximate distance oracles for vertex-labeled planar graphs, enabling fast queries and updates with minimal space, enhancing graph analysis capabilities.

Contribution

It presents three novel dynamic approximate distance oracles for vertex-labeled planar graphs with polylogarithmic query/update times and nearly linear space.

Findings

All oracles support fast query and update operations.

They achieve near-linear space complexity.

The methods improve efficiency over previous approaches.

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.