  An important area of combinatorial optimization is the study of packing and
covering problems, such as Bin Packing, Multiple Knapsack, and Bin Covering.
Those problems have been studied extensively from the viewpoint of
approximation algorithms, but their parameterized complexity has only been
investigated barely. For problem instances containing no "small" items,
classical matching algorithms yield optimal solutions in polynomial time. In
this paper we approach them by their distance from triviality, measuring the
problem complexity by the number $k$ of small items.
  Our main results are fixed-parameter algorithms for vector versions of Bin
Packing, Multiple Knapsack, and Bin Covering parameterized by $k$. The
algorithms are randomized with one-sided error and run in time $4^{k} \cdot k!
\cdot n^{O(1)}$. To achieve this, we introduce a colored matching problem to
which we reduce all these packing problems. The colored matching problem is
natural in itself and we expect it to be useful for other applications. We also
present a deterministic fixed-parameter for Bin Packing with run time
$(k!)^{2}\cdot k \cdot 2^{k}\cdot n\cdot \log(n)$.
