eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2017-12-07
4:1
4:12
10.4230/LIPIcs.ISAAC.2017.4
article
Placing your Coins on a Shelf
Alt, Helmut
Buchin, Kevin
Chaplick, Steven
Cheong, Otfried
Kindermann, Philipp
Knauer, Christian
Stehn, Fabian
We consider the problem of packing a family of disks 'on a shelf,'
that is, such that each disk touches the x-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(n log n) time, and provide an 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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol092-isaac2017/LIPIcs.ISAAC.2017.4/LIPIcs.ISAAC.2017.4.pdf
packing problems
approximation algorithms
NP-hardness