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Register a new userAn efficient algorithm for finding all possible input nodes for controlling complex networks
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Added by
Xizhe Zhang
Publication date
2017
fields
Informatics Engineering
and research's language is
English
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Understanding structural controllability of a complex network requires to identify a Minimum Input nodes Set (MIS) of the network. It has been suggested that finding an MIS is equivalent to computing a maximum matching of the network, where the unmatched nodes constitute an MIS. However, maximum matching of a network is often not unique, and finding all MISs may provide deep insights to the controllability of the network. Finding all possible input nodes, which form the union of all MISs, is computationally challenging for large networks. Here we present an efficient enumerative algorithm for the problem. The main idea is to modify a maximum matching algorithm to make it efficient for finding all possible input nodes by computing only one MIS. We rigorously proved the correctness of the new algorithm and evaluated its performance on synthetic and large real networks. The experimental results showed that the new algorithm ran several orders of magnitude faster than the existing method on large real networks.
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Controlling a complex network towards a desired state is of great importance in many applications. A network can be controlled by inputting suitable external signals into some selected nodes, which are called driver nodes. Previous works found there exist two control modes in dense networks: distributed and centralized modes. For networks with the distributed mode, most of the nodes can be act as driver nodes; and those with the centralized mode, most of the nodes never be the driver nodes. Here we present an efficient algorithm to change the control type of nodes, from input nodes to redundant nodes, which is done by reversing edges of the network. We conclude four possible cases when reversing an edge and show the control mode can be changed by reversing very few in-edges of driver nodes. We evaluate the performance of our algorithm on both synthetic and real networks. The experimental results show that the control mode of a network can be easily changed by reversing a few elaborately selected edges, and the number of possible driver nodes is dramatically decreased. Our methods provide the ability to design the desired control modes of the network for different control scenarios, which may be used in many application regions.
The ability to control a complex network towards a desired behavior relies on our understanding of the complex nature of these social and technological networks. The existence of numerous control schemes in a network promotes us to wonder: what is the underlying relationship of all possible input nodes? Here we introduce input graph, a simple geometry that reveals the complex relationship between all control schemes and input nodes. We prove that the node adjacent to an input node in the input graph will appear in another control scheme, and the connected nodes in input graph have the same type in control, which they are either all possible input nodes or not. Furthermore, we find that the giant components emerge in the input graphs of many real networks, which provides a clear topological explanation of bifurcation phenomenon emerging in dense networks and promotes us to design an efficient method to alter the node type in control. The findings provide an insight into control principles of complex networks and offer a general mechanism to design a suitable control scheme for different purposes.
195 -
Christian M. Schneider
, Tobias A. Kesselring
, Jose S. Andrade Jr. andn Hans J. Herrmann
2012
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