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arXiv · 2503.18425

Faster Construction of a Planar Distance Oracle with Õ(1) Query Time

Itai Boneh·Shay Golan·Shay Mozes·Daniel Prigan·Oren Weimann
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Abstract

We show how to preprocess a weighted undirected $n$-vertex planar graph in $\tilde O(n^{4/3})$ time, such that the distance between any pair of vertices can then be reported in $\tilde O(1)$ time. This improves the previous $\tilde O(n^{3/2})$ preprocessing time [JACM'23]. Our main technical contribution is a near optimal construction of \emph{additively weighted Voronoi diagrams} in undirected planar graphs. Namely, given a planar graph $G$ and a face $f$, we show that one can preprocess $G$ in $\tilde O(n)$ time such that given any weight assignment to the vertices of $f$ one can construct the additively weighted Voronoi diagram of $f$ in near optimal $\tilde O(|f|)$ time. This improves the $\tilde O(\sqrt{n |f|})$ construction time of [JACM'23].

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Itai Boneh, Shay Golan, Shay Mozes, Daniel Prigan, Oren Weimann. 2025-03-24. Faster Construction of a Planar Distance Oracle with Õ(1) Query Time. https://arxiv.org/abs/2503.18425

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