Corpus ID: 3511670

# Voronoi diagrams on planar graphs, and computing the diameter in deterministic $\tilde{O}(n^{5/3})$ time

@article{Gawrychowski2017VoronoiDO,
title={Voronoi diagrams on planar graphs, and computing the diameter in deterministic \$\tilde\{O\}(n^\{5/3\})\$ time},
author={Pawel Gawrychowski and Haim Kaplan and S. Mozes and M. Sharir and Oren Weimann},
journal={arXiv: Data Structures and Algorithms},
year={2017}
}
We present an explicit and efficient construction of additively weighted Voronoi diagrams on planar graphs. Let $G$ be a planar graph with $n$ vertices and $b$ sites that lie on a constant number of faces. We show how to preprocess $G$ in $\tilde O(nb^2)$ time (footnote: The $\tilde O$ notation hides polylogarithmic factors.) so that one can compute any additively weighted Voronoi diagram for these sites in $\tilde O(b)$ time. We use this construction to compute the diameter of a directed… Expand
3 Citations
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