2026-08-16T20:14:58Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:8214 2024-03-06T10:41:45Z ddc:004 open_access

Placing your Coins on a Shelf Alt, Helmut Buchin, Kevin Chaplick, Steven Cheong, Otfried Kindermann, Philipp Knauer, Christian Stehn, Fabian packing problems approximation algorithms NP-hardness 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Helmut Alt and Kevin Buchin and Steven Chaplick and Otfried Cheong and Philipp Kindermann and Christian Knauer and Fabian Stehn 2017 Is Part Of LIPIcs, Volume 92, 28th International Symposium on Algorithms and Computation (ISAAC 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ISAAC.2017.4 urn:nbn:de:0030-drops-82145 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.4 eng https://creativecommons.org/licenses/by/3.0/legalcode