Dynamic Planar Voronoi Diagrams for General Distance Functions and their Algorithmic Applications

@inproceedings{Kaplan2017DynamicPV,
  title={Dynamic Planar Voronoi Diagrams for General Distance Functions and their Algorithmic Applications},
  author={Haim Kaplan and Wolfgang Mulzer and Liam Roditty and Paul Seiferth and Micha Sharir},
  booktitle={SODA},
  year={2017}
}
We describe a new data structure for dynamic nearest neighbor queries in the plane with respect to a general family of distance functions that includes Lp-norms and additively weighted Euclidean distances, and for general (convex, pairwise disjoint) sites that have constant description complexity (line segments, disks, etc.). Our data structure has a polylogarithmic update and query time, improving an earlier data structure of Agarwal, Efrat and Sharir that required O(n) time for an update and… CONTINUE READING
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