  The problem of packing of equal disks (or circles) into a rectangle is a
fundamental geometric problem. (By a packing here we mean an arrangement of
disks in a rectangle without overlapping.) We consider the following
algorithmic generalization of the equal disk packing problem. In this problem,
for a given packing of equal disks into a rectangle, the question is whether by
changing positions of a small number of disks, we can allocate space for
packing more disks. More formally, in the repacking problem, for a given set of
$n$ equal disks packed into a rectangle and integers $k$ and $h$, we ask
whether it is possible by changing positions of at most $h$ disks to pack $n+k$
disks. Thus the problem of packing equal disks is the special case of our
problem with $n=h=0$.
  While the computational complexity of packing equal disks into a rectangle
remains open, we prove that the repacking problem is NP-hard already for $h=0$.
Our main algorithmic contribution is an algorithm that solves the repacking
problem in time $(h+k)^{O(h+k)}\cdot |I|^{O(1)}$, where $I$ is the input size.
That is, the problem is fixed-parameter tractable parameterized by $k$ and $h$.
