Placing your Coins on a Shelf

Helmut Alt, Kevin Buchin, Steven Chaplick, Otfried Cheong, Philipp Kindermann, Christian Knauer, Fabian Stehn

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingAcademicpeer-review

Abstract

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.

Original languageEnglish
Title of host publication28th International Symposium on Algorithms and Computation (ISAAC 2017)
EditorsYoshio Okamoto, Takeshi Tokuyama
PublisherSchloss Dagstuhl - Leibniz-Zentrum fuer Informatik
Pages4:1-4:12
Volume92
DOIs
Publication statusPublished - 2017
Externally publishedYes

Publication series

SeriesLeibniz International Proceedings in Informatics (LIPIcs)
Volume92
ISSN1868-8969

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