Shortest paths and centrality in uncertain networks

Computing the shortest path between a pair of nodes is a fundamental graph primitive, which has critical applications in vehicle routing, finding functional pathways in biological networks, survivable network design, among many others. In this work, we study shortest-path queries over uncertain networks, i.e., graphs where every edge is associated with a probability of existence. We show that, for a given path, it is # P -hard to compute the probability of it being the shortest path, and we also derive other interesting properties highlighting the complexity of computing the Most Probable Shortest Paths (MPSPs). We thus devise sampling-based efficient algorithms, with end-to-end accuracy guarantees, to compute the MPSP. As a concrete application, we show how to compute a novel concept of betweenness centrality in an uncertain graph using MPSPs. Our thorough experimental results and rich real-world case studies on sensor networks and brain networks validate the effectiveness, efficiency, scalability, and usefulness of our solution.

Finite time synchronization diffusion of uncertain networks with the switching topology

The finite time synchronization diffusion of uncertain networks with the switching topology is investigated in this paper. Spatiotemporal chaotic systems as nodes to construct the network, and the topology of network can jump from one construction to another to meet the actual demand. It is not like ordinary synchronization of network, our method can realize synchronization diffusion originated from boundary conditions, and the diffusion step can be determined by Taylor expand. The parameters are identified through proposed scheme against parameter uncertainties of system in practice. Numerical simulations are utilized to demonstrate the correctness and effectiveness of the finite time synchronization diffusion criteria. In the section of analysis and discussion, we have analyzed the impact of synchronization diffusion step and controller on the synchronization diffusion time.

Synchronization control between discrete uncertain networks with different topologies

Based on open-loop–closed-loop technology, we researched the outer synchronization between discrete uncertain networks with different topologies. In order to make the drive and response networks realize the synchronization, a special Lyapunov function is constructed and the open-loop–closed-loop controller is designed. At the same time, we designed an effective parameter identification law to accurately identify the uncertain parameters in the response network. The simulation results show that the synchronization strategy is simple and practical.