The union of unit balls has quadratic complexity, even if they all contain the origin
<|reference_start|>The union of unit balls has quadratic complexity, even if they all contain the origin: 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.<|reference_end|>
@article{bronnimann1999the,
    title={The union of unit balls has quadratic complexity, even if they all
  contain the origin},
    author={Herve Bronnimann, Olivier Devillers},
    journal={arXiv preprint arXiv:cs/9907025},
    year={1999},
    archivePrefix={arXiv},
    eprint={cs/9907025},
    primaryClass={cs.CG}
}