  In this paper, we show an improved bound and new algorithm for the online
square-into-square packing problem. This two-dimensional packing problem
involves packing an online sequence of squares into a unit square container
without any two squares overlapping. The goal is to find the largest area
$\alpha$ such that any set of squares with total area $\alpha$ can be packed.
We show an algorithm that can pack any set of squares with total area $\alpha
\leq 3/8$ into a unit square in an online setting, improving the previous bound
of $11/32$.
