Packing Disks into Disks with Optimal Worst-Case Density
Computational Geometry
2019-03-20 v1
Abstract
We provide a tight result for a fundamental problem arising from packing disks into a circular container: The critical density of packing disks in a disk is 0.5. This implies that any set of (not necessarily equal) disks of total area can always be packed into a disk of area 1; on the other hand, for any there are sets of disks of area that cannot be packed. The proof uses a careful manual analysis, complemented by a minor automatic part that is based on interval arithmetic. Beyond the basic mathematical importance, our result is also useful as a blackbox lemma for the analysis of recursive packing algorithms.
Cite
@article{arxiv.1903.07908,
title = {Packing Disks into Disks with Optimal Worst-Case Density},
author = {Sándor P. Fekete and Phillip Keldenich and Christian Scheffer},
journal= {arXiv preprint arXiv:1903.07908},
year = {2019}
}