  We present a $\frac74$ approximation algorithm for the matching augmentation
problem (MAP): given a multi-graph with edges of cost either zero or one such
that the edges of cost zero form a matching, find a 2-edge connected spanning
subgraph (2-ECSS) of minimum cost.
  We first present a reduction of any given MAP instance to a collection of
well-structured MAP instances such that the approximation guarantee is
preserved. Then we present a $\frac74$ approximation algorithm for a
well-structured MAP instance. The algorithm starts with a min-cost 2-edge cover
and then applies ear-augmentation steps. We analyze the cost of the
ear-augmentations using an approach similar to the one proposed by Vempala and
Vetta for the (unweighted) min-size 2-ECSS problem (`Factor 4/3 approximations
for minimum 2-connected subgraphs,' APPROX 2000, LNCS 1913, pp.262-273).
