Search for minimal paths in modified networks

The problem of searching for all minimal paths (MPs) in a network obtained by modifying the original network, e.g. for network expansion or reinforcement, is discussed and solved in this study. The existing best-known method to solve this problem was a straightforward approach. It needed extensive comparison and verification, and failed to solve some special but important cases. Therefore, a more efficient, intuitive and generalized method to search for all MPs without an extensive research procedure is proposed. In this presentation, first we develop an intuitive algorithm based upon the reformation of all MPs in the original network to search for all MPs in a modified network. Next, the computational complexity of the proposed algorithm is analyzed and compared with the existing methods. Finally, examples illustrate how all MPs are generated in a modified network based upon the reformation of all of the MPs in the corresponding original network.