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An improved algorithm for finding all minimal paths in a network

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  • Bai, Guanghan
  • Tian, Zhigang
  • Zuo, Ming J.

Abstract

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.

Suggested Citation

  • Bai, Guanghan & Tian, Zhigang & Zuo, Ming J., 2016. "An improved algorithm for finding all minimal paths in a network," Reliability Engineering and System Safety, Elsevier, vol. 150(C), pages 1-10.
    • Handle: RePEc:eee:reensy:v:150:y:2016:i:c:p:1-10
    DOI: 10.1016/j.ress.2016.01.011
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    References listed on IDEAS

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    1. Bai, Guanghan & Zuo, Ming J. & Tian, Zhigang, 2015. "Search for all d-MPs for all d levels in multistate two-terminal networks," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 300-309.
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    Cited by:

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    2. Niu, Yi-Feng & Wan, Xiao-Yu & Xu, Xiu-Zhen & Ding, Dong, 2020. "Finding all multi-state minimal paths of a multi-state flow network via feasible circulations," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    3. Yi-Kuei Lin & Cheng-Fu Huang & Chin-Chia Chang, 2022. "Reliability of spare routing via intersectional minimal paths within budget and time constraints by simulation," Annals of Operations Research, Springer, vol. 312(1), pages 345-368, May.
    4. Ping-Chen Chang, 2022. "Reliability evaluation and big data analytics architecture for a stochastic flow network with time attribute," Annals of Operations Research, Springer, vol. 311(1), pages 3-18, April.
    5. Yi-Kuei Lin & Lance Fiondella & Ping-Chen Chang, 2022. "Reliability of time-constrained multi-state network susceptible to correlated component faults," Annals of Operations Research, Springer, vol. 311(1), pages 239-254, April.
    6. Majid Forghani-elahabad & Omar Mutab Alsalami, 2023. "Using a Node–Child Matrix to Address the Quickest Path Problem in Multistate Flow Networks under Transmission Cost Constraints," Mathematics, MDPI, vol. 11(24), pages 1-15, December.
    7. Liu, Tao & Bai, Guanghan & Tao, Junyong & Zhang, Yun-An & Fang, Yining & Xu, Bei, 2022. "Modeling and evaluation method for resilience analysis of multi-state networks," Reliability Engineering and System Safety, Elsevier, vol. 226(C).
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    9. Yi-Kuei Lin & Thi-Phuong Nguyen & Louis Cheng-Lu Yeng, 2022. "Reliability evaluation of a stochastic multimodal transport network under time and budget considerations," Annals of Operations Research, Springer, vol. 312(1), pages 369-387, May.
    10. Xu, Bei & Liu, Tao & Bai, Guanghan & Tao, Junyong & Zhang, Yun-an & Fang, Yining, 2022. "A multistate network approach for reliability evaluation of unmanned swarms by considering information exchange capacity," Reliability Engineering and System Safety, Elsevier, vol. 219(C).

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