Table 1 Our greedy algorithm for constructing target control tree for network G(V, E)

Input: Network G(V, E), target nodes O

Initialize:

B₀ ←(R₀, L₀) //the right side R₀ is made of target nodes O, and the left side L₀ is made of nodes from which the targes could be reachable.

m ₀ ←Matching(B₀) //Find maximum matching m ₀ among bipartite graph B₀

CF(V₀, m₀) ←Subgraph(V₀, m₀) // Let V₀ = R₀∪L₀, we obtain a subgraph CF(V₀, m₀)

for paired nodes (v_i⁰,v_j⁰)∈CF(V₀, m₀) do // if we could find a path from node v_i⁰∈L₀ to v_j⁰∈R₀, add edge e_k⁰ = (v_i⁰,v_j⁰) to TCT .

E₀← E₀∪e_k⁰

end

While L _n ≠ ∅  (n ≥ 1) do

R _n ← L _n-1 //Let the set of nodes in L _n-1 to be the new R _n set

B _n ←(R_n, L_n) //get a new bipartite graph B _n .

m _n ←Matching(B_n) //Calculate a maximum matching m _n in B _n

V _n  = V _n-1 ∪L _n

CF(V _n , m _n ) ←Subgraph(V _n , m _n )

for paired nodes (v_iⁿ,v_jⁿ)∈CF(V _n , m _n ) do // v_iⁿ∈L_n, v_jⁿ∈R _n

If there exists a directed path from v_iⁿ to v_jⁿ _,

add edge e_kⁿ = (v_iⁿ,v_jⁿ) to TCT.

Let E_n = E_n-1∪(∪e_kⁿ).

End

Output: The target control tree, TCT ≡ (V _TCT , E _TCT ) = (V _n , E _n )