New path-reporting vertex-label distance oracles achieve stretch (4k-5)(1+ε) with near-linear size or optimal stretch 2k-1 with mildly higher query time.
(1 +ϵ)-distance oracles for vertex-labeled planar graphs
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Path-Reporting Distance Oracles for Vertex-Labeled Graphs
New path-reporting vertex-label distance oracles achieve stretch (4k-5)(1+ε) with near-linear size or optimal stretch 2k-1 with mildly higher query time.