The Feedback Vertex Set Problem of Multiplex Networks

The feedback vertex set (FVS) problem of network aims to find a vertex subset of smallest size that contains at least one vertex of each cycle of the network. The FVS problem has found wide applications, ranging from circuit design, network security and network control and observation etc. However, the majority of existing studies on FVS problem are confined to single networks. In this brief, under the consideration of one kind of control problem of multiplex network, we introduce the concept of FVS of multiplex network. The control problem of multiplex network is naturally mapped into the FVS problem of multiplex network. We then propose two simulated annealing (SA) algorithms to solve the directed FVS problem of multiplex network and undirected FVS problem of multiplex network respectively. The effectiveness of the SA algorithms is finally verified on both artificial multiplex networks and real-world multiplex networks.