The union of unit balls has quadratic complexity, even if they all contain the origin
Herve Bronnimann, Olivier Devillers
TL;DR
This paper proves that the union of unit balls in three-dimensional space can have quadratic complexity, even when all balls contain the origin, resolving a longstanding conjecture.
Contribution
It provides a lower bound construction demonstrating quadratic complexity of the union of unit balls in 3D, settling Sharir's conjecture.
Findings
Union of unit balls in 3D can have quadratic complexity
All balls containing the origin does not reduce complexity
Confirms a conjecture by Sharir
Abstract
We provide a lower bound construction showing that the union of unit balls in three-dimensional space has quadratic complexity, even if they all contain the origin. This settles a conjecture of Sharir.
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.
Taxonomy
TopicsPoint processes and geometric inequalities · Quasicrystal Structures and Properties · Mathematics and Applications