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Sublinear Explicit Incremental Planar Voro Sublinear Explicit Incremental Planar Voronoi Diagrams noi Diagrams

par Arseneva, Elena;Iacono, John ;Koumoutsos, Grigorios ;Langerman, Stefan ;Zolotov, Boris
Référence arXiv.org
Publication Publié, 2020-06-01

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Résumé :

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 O~(N3/4) expected amortized time, where O~ suppresses polylogarithmic terms. This is the first result to achieve sublinear time insertions; previously it was shown by Allen et al. that Θ(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.