Connectivity probability evaluation of a large-scale highway bridge network using network decomposition

The existing NP-hard problem makes it difficult to evaluate the connectivity probability of large-scale networks, causing great barriers to evaluating and ensuring network safety. In this study, the connectivity probability for a highway bridge network composed of 1772 bridges is evaluated using network decomposition. First, the multilevel k-way graph partition is employed recursively to decompose the network into several approximately equally-sized subnetworks and minimum edge-cuts in series. Then, the decomposed network connectivity probability could be achieved in two steps: subnet and simplified network evaluations. In the subnet evaluation step, the subnet states with and without edge-cuts are judged respectively. Different from the existing connec-tivity binary definition as connected or disconnected, three states are redefined using adjacent matrices for each subnet: subnet with and without edge-cuts both connected (CCS), both disconnected (DDS), subnet with edge -cuts connected while without edge-cuts disconnected (DCS). For DDS would inevitably lead to the disconnec-tion of the bridge network, such state wouldn't be enumerated in the following step for efficiency, while the CCS and DCS would be further represented by the terminal nodes. In the simplified network evaluation step, the highway bridge network connectivity can be thoroughly represented by treating terminal nodes and edge-cuts as a serial simplified network whose connectivity probability could be calculated by analysing the limited states. The connectivity probability evaluation shows high efficiency and accuracy in the investigated bridge network.