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arXiv · 2009.14716

Truly Subquadratic Exact Distance Oracles with Constant Query Time for Planar Graphs

Viktor Fredslund-Hansen·Shay Mozes·Christian Wulff-Nilsen
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Abstract

Given an undirected, unweighted planar graph $G$ with $n$ vertices, we present a truly subquadratic size distance oracle for reporting exact shortest-path distances between any pair of vertices of $G$ in constant time. For any $\varepsilon > 0$, our distance oracle takes up $O(n^{5/3+\varepsilon})$ space and is capable of answering shortest-path distance queries exactly for any pair of vertices of $G$ in worst-case time $O(\log (1/\varepsilon))$. Previously no truly sub-quadratic size distance oracles with constant query time for answering exact all-pairs shortest paths distance queries existed.

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Viktor Fredslund-Hansen, Shay Mozes, Christian Wulff-Nilsen. 2020-09-30. Truly Subquadratic Exact Distance Oracles with Constant Query Time for Planar Graphs. https://arxiv.org/abs/2009.14716

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