Fig. 1
Demonstration of the limitations of the existed methods for the target control problem with objectives-guided optimization. a Two simple networks. In the two networks, the target set is {v3,v4, v6,v7} and {v3,v4, v6} respectively (highlighted in green) and the constrained nodes set is {v2,v4} and {v1} respectively (shape in hexagon). Here we want to minimum the quantity of driver nodes to control the target nodes set {v3,v4, v6,v7} and {v3,v4, v6} (i.e., disease-associated genes) and maximum the identified driver nodes within the constrained nodes (i.e., practical constraints as prior known drug targets). b By applying full control of Liu’s method to the two networks, we can identify the unmatched nodes {v1,v3,v5} and {v1,v2} (nodes within the blue circle) in the right side of the bipartite graph transferred from the directed network, as the driver nodes(more details seen in ref. [6]). c By using target control of Gao’s method, they first obtain the updated bipartite graph by choosing the nodes in the left side in the previous matching (highlighted in grape) as the nodes in the right side of the current matching (highlighted in green) and then calculate a maximum matching in the updated bipartite graph. Finally they add unmatched nodes (nodes within the blue circle) in right side of the updated bipartite graph to the set of driver nodes (more details seen in ref. [8]), which identify the set of driver nodes of the two networks as {v1,v3,v4} and {v1,v2}. In the simple example 1, according to the k-walk theory in Re. [8], it is easy to know that node v2 can control v3 and v6 and v4 can control v4 and v6. For the simple example 2, based on the fact that when we remove a link it will not decrease the quantity of driver nodes. For example, when we remove the link from node v4 to node v3 in Fig. 2, according to the k-walk theory in Re. [8], it is easy to know that node v1 can control v3, v4 and v6. Therefore, the nodes {v2,v4} and {v1} as the optional driver nodes are ignored by the existed methods for the two networks