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- W3204243990 abstract "Given an undirected $n$-vertex planar graph $G=(V,E,omega)$ with non-negative edge weight function $omega:Erightarrow mathbb R$ and given an assigned label to each vertex, a vertex-labeled distance oracle is a data structure which for any query consisting of a vertex $u$ and a label $lambda$ reports the shortest path distance from $u$ to the nearest vertex with label $lambda$. We show that if there is a distance oracle for undirected $n$-vertex planar graphs with non-negative edge weights using $s(n)$ space and with query time $q(n)$, then there is a vertex-labeled distance oracle with $tilde{O}(s(n))$ space and $tilde{O}(q(n))$ query time. Using the state-of-the-art distance oracle of Long and Pettie, our construction produces a vertex-labeled distance oracle using $n^{1+o(1)}$ space and query time $tilde O(1)$ at one extreme, $tilde O(n)$ space and $n^{o(1)}$ query time at the other extreme, as well as such oracles for the full tradeoff between space and query time obtained in their paper. This is the first non-trivial exact vertex-labeled distance oracle for planar graphs and, to our knowledge, for any interesting graph class other than trees." @default.
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- W3204243990 date "2021-09-30" @default.
- W3204243990 modified "2023-09-27" @default.
- W3204243990 title "Near-Optimal Distance Oracles for Vertex-Labeled Planar Graphs" @default.
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