Incremental Voronoi Diagrams
Sarah R. Allen, Luis Barba, John Iacono, Stefan Langerman

TL;DR
This paper investigates the incremental update complexity of Voronoi diagrams, establishing tight bounds, and introduces a semi-dynamic data structure that efficiently maintains the diagram's structure for convex site sets.
Contribution
It provides tight bounds on the amortized number of edge updates needed for incremental Voronoi diagram construction and presents a novel data structure supporting efficient updates and queries.
Findings
Amortized edge update cost is O(√n) per site insertion.
Matching lower bound of Ω(√n) for edge updates even in tree diagrams.
Data structure supports point location and neighbor queries efficiently.
Abstract
We study the amortized number of combinatorial changes (edge insertions and removals) needed to update the graph structure of the Voronoi diagram (and several variants thereof) of a set of sites in the plane as sites are added. We define a general update operation for planar graphs modeling the incremental construction of several variants of Voronoi diagrams as well as the incremental construction of an intersection of halfspaces in . We show that the amortized number of edge insertions and removals needed to add a new site is . A matching combinatorial lower bound is shown, even in the case where the graph of the diagram is a tree. This contrasts with the upper bound of Aronov et al. (2006) for farthest-point Voronoi diagrams when the points are inserted in order along their convex hull. We present…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
