An improved d-MP search algorithm for multi-state networks

A Minimal Path (MP) vector for a system state d is called a d-MP. Most reported works on generating d-MPs are for a particular d value. If all d-MPs for all possible integer d values are required, we need to call those methods multiple times with respect to all d values. Virtually, each d-MP candidate can be generated by a combination of one (d-1)-MP and one binary minimal path vector. Thus, we can use binary MP vectors as building blocks to generate 2-MP candidates, and use 2-MPs and binary MPs as building blocks to generate 3-MP candidates ... and so forth. During the process, each newly generated candidate will be validated by certain constraints and real d-MPs are obtained. When the d-MPs with the maximum d value have been found, all the d-MPs for all possible integer d value are found as well. Based on the observations above, we report a recursive algorithm based on the concept of backtracking. By computational experiments, it is found that the proposed algorithm is more efficient than existing algorithms for finding all d-MPs for all possible integer d values. The generated d-MPs can be used for system state distribution evaluation.