  We give an asymptotic approximation scheme (APTAS) for the problem of packing
a set of circles into a minimum number of unit square bins. To obtain rational
solutions, we use augmented bins of height $1+\gamma$, for some arbitrarily
small number $\gamma > 0$. Our algorithm is polynomial on $\log 1/\gamma$, and
thus $\gamma$ is part of the problem input. For the special case that $\gamma$
is constant, we give a (one dimensional) resource augmentation scheme, that is,
we obtain a packing into bins of unit width and height $1+\gamma$ using no more
than the number of bins in an optimal packing. Additionally, we obtain an APTAS
for the circle strip packing problem, whose goal is to pack a set of circles
into a strip of unit width and minimum height. These are the first
approximation and resource augmentation schemes for these problems.
  Our algorithm is based on novel ideas of iteratively separating small and
large items, and may be extended to a wide range of packing problems that
satisfy certain conditions. These extensions comprise problems with different
kinds of items, such as regular polygons, or with bins of different shapes,
such as circles and spheres. As an example, we obtain APTAS's for the problems
of packing d-dimensional spheres into hypercubes under the $L_p$-norm.
