English

Placing your Coins on a Shelf

Computational Geometry 2018-09-10 v2 Metric Geometry

Abstract

We consider the problem of packing a family of disks "on a shelf", that is, such that each disk touches the xx-axis from above and such that no two disks overlap. We prove that the problem of minimizing the distance between the leftmost point and the rightmost point of any disk is NP-hard. On the positive side, we show how to approximate this problem within a factor of 4/3 in O(nlogn)O(n \log n) time, and provide an O(nlogn)O(n \log n)-time exact algorithm for a special case, in particular when the ratio between the largest and smallest radius is at most four.

Keywords

Cite

@article{arxiv.1707.01239,
  title  = {Placing your Coins on a Shelf},
  author = {Helmut Alt and Kevin Buchin and Steven Chaplick and Otfried Cheong and Philipp Kindermann and Christian Knauer and Fabian Stehn},
  journal= {arXiv preprint arXiv:1707.01239},
  year   = {2018}
}

Comments

Appeared at Proc. 28th International Symposium on Algorithms and Computation (ISAAC 2017)

R2 v1 2026-06-22T20:38:12.733Z