Title: Placing your Coins on a Shelf,
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.