  In this paper, we reduce the maximum weighted matching problem to the largest
cardinality matching in {\bf CONGEST}. The paper presents two technical
contributions. The first of them is a simple $poly(\log n,
\frac{1}{\varepsilon}, t, \ln w_t)$-round {\bf CONGEST} algorithm for reducing
the maximum weighted matching problem to the largest cardinality matching
problem. This is achieved under the assumption that all vertices know all
edge-weights $\{w_1,....,w_t\}$ (in particular, they know $t$, the number of
different edge-weights), though a particular vertex may not know the weight of
a particular edge. Our second ingredient is a simple rounding algorithm
(similar to approximation algorithms for the bin packing problem) allowing to
reduce general instances of the maximum weighted matching problem to ones
satisfying the assumptions of the first ingredient, in which $t\leq poly'(\log
n, \frac{1}{\varepsilon})$. We end the paper with a brief discussion of
implementing our algorithms in {\bf CONGEST}. Our main conclusion is that we
just need constant rounds for the reduction.
