Finding minimum number of edges such that when adding into the graph, the graph is a 2-connected graph Given is a undirected and 1-connected graph G=(V,E). Between every two node b=(u,v) in graph G there is a cost c_b to build another edge(Regardless of whether (u,v) ∈E or not). We use a C={c_b |c_b∈Z^+,b∈V×V} to represent costs between every node regardless of whether (u,v) ∈E or not. Now, we want to add some edges M⊂E into the graph G which makes graph G^'=G+M is a 2-connected graph (G^' allow the appearance of multiple edges while graph G is not) such that weights of edge set of M is minimize.
$2$-connectedness is the same as bridgeless.

So $M$ must be the set of bridges in $G$ no matter how large or small their sum is.