Sublinear Explicit Incremental Planar Voronoi Diagrams

Elena Arseneva; John Iacono; Grigorios Koumoutsos; Stefan Langerman; Boris Zolotov

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arXiv · 2007.01686

Sublinear Explicit Incremental Planar Voronoi Diagrams

Elena Arseneva·John Iacono·Grigorios Koumoutsos·Stefan Langerman·Boris Zolotov

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Abstract

A data structure is presented that explicitly maintains the graph of a Voronoi diagram of $N$ point sites in the plane or the dual graph of a convex hull of points in three dimensions while allowing insertions of new sites/points. Our structure supports insertions in $\tilde O (N^{3/4})$ expected amortized time, where $\tilde O$ suppresses polylogarithmic terms. This is the first result to achieve sublinear time insertions; previously it was shown by Allen et al. that $\Theta(\sqrt{N})$ amortized combinatorial changes per insertion could occur in the Voronoi diagram but a sublinear-time algorithm was only presented for the special case of points in convex position.

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Elena Arseneva, John Iacono, Grigorios Koumoutsos, Stefan Langerman, Boris Zolotov. 2020-07-03. Sublinear Explicit Incremental Planar Voronoi Diagrams. https://arxiv.org/abs/2007.01686

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