%0 Journal Article %1 abcckks-pycos-jocg18 %A Alt, Helmut %A Buchin, Kevin %A Chaplick, Steven %A Cheong, Otfried %A Kindermann, Philipp %A Knauer, Christian %A Stehn, Fabian %D 2018 %J Journal of Computational Geometry %K myown %N 1 %P 312--327 %R 10.20382/jocg.v9i1a10 %T Placing your Coins on a Shelf %V 9 %X We consider the problem of packing a family of disks ön 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 $O(n n)$ time, and provide an $O(n n)$-time exact algorithm for a special case, in particular when the ratio between the largest and smallest radius is at most four.

@article{abcckks-pycos-jocg18, 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.}, added-at = {2018-08-21T18:05:20.000+0200}, arxiv = {https://arxiv.org/abs/1707.01239}, author = {Alt, Helmut and Buchin, Kevin and Chaplick, Steven and Cheong, Otfried and Kindermann, Philipp and Knauer, Christian and Stehn, Fabian}, biburl = {https://www.bibsonomy.org/bibtex/23b7edfd4ccec32c2c19bf454585554fc/kindermann}, doi = {10.20382/jocg.v9i1a10}, interhash = {6ccaa5c2e43fdf2fa14f979d0dd11b4c}, intrahash = {3b7edfd4ccec32c2c19bf454585554fc}, journal = {Journal of Computational Geometry}, keywords = {myown}, number = 1, pages = {312--327}, timestamp = {2018-09-18T07:36:06.000+0200}, title = {Placing your Coins on a Shelf}, volume = 9, year = 2018 }