We consider the problem of communication network expansion and upgrading, which is abstracted as the capacity expansion problem of spanning arborescence with constraints (CEPAC) in directed networks. Firstly, we prove that CEPAC problem is NP-hard by constructing an instance of CEPAC based on 0-1 knapsack problem. Secondly, by Megiddo parameter search of the spanning tree and Megiddo parameter search strategy of matroid intersection, we establish the relationship between the spanning arborescence polytope and the matroid intersection, and transform an optimal spanning arborescence into an adjacent optimal spanning arborescence through the basic transformation. Then, we design a $(2,1)$-approximate matroid intersection algorithm with constraints for CEPAC problem. Finally, we discuss the capacity expansion problem minimum arborescence (CEPMA) and solve it by modifying Chu-Liu-Edmonds algorithm with lexicographical order.