minimum cardinality maximal matching of graph
A 2-approximation can be obtained by returning a maximal matching, Call it M.
Let OPT be a minimum maximal matching then for each edge in M OPT covers at least one of its endpoints thus: |OPT|>=|M|/2
It would be better if you’ll be more explicit about what you did and what you’d like the algorithm to achieve (analysis of your idea, approximation factor, so on...)