An improved algorithm for finding all minimal paths in a network

• A linked path structure indexed by nodes is introduced to represent networks.
• Additional conditions for backtracking are proposed based on the distance of each node.
• An efficient algorithm is developed to find all MPs for two-terminal networks.
• The computational efficiency of the algorithm for two-terminal networks is investigated.
• The computational efficiency of the algorithm for multi-terminal networks is investigated.

Minimal paths (MPs) play an important role in network reliability evaluation. In this paper, we report an efficient recursive algorithm for finding all MPs in two-terminal networks, which consist of a source node and a sink node. A linked path structure indexed by nodes is introduced, which accepts both directed and undirected form of networks. The distance between each node and the sink node is defined, and a simple recursive algorithm is presented for labeling the distance for each node. Based on the distance between each node and the sink node, additional conditions for backtracking are incorporated to reduce the number of search branches. With the newly introduced linked node structure, the distances between each node and the sink node, and the additional backtracking conditions, an improved backtracking algorithm for searching for all MPs is developed. In addition, the proposed algorithm can be adapted to search for all minimal paths for each source–sink pair in networks consisting of multiple source nodes and/or multiple sink nodes. Through computational experiments, it is demonstrated that the proposed algorithm is more efficient than existing algorithms when the network size is not too small. The proposed algorithm becomes more advantageous as the size of the network grows.