Incremental network design with minimum spanning trees

Given an edge-weighted graph <i>G</i>=(<i>V,E</i>) and a set <i>E</i>₀⊂<i>E</i>, the incremental network design problem with minimum spanning trees asks for a sequence of edges <i>e′</i>₁,…,<i>e′_T</i>∈<i>E</i>∖<i>E</i>₀ minimizing [formula could not be replicated] where <i>w</i>(<i>Xt</i>) is the weight of a minimum spanning tree <i>X_t</i> for the subgraph (<i>V,E</i>₀∪{<i>e′</i>₁,…,<i>e′_t</i>}) and <i>T</i>=|<i>E</i>∖<i>E</i>₀|. We prove that this problem can be solved by a greedy algorithm.