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Finding all multi-state minimal paths of a multi-state flow network via feasible circulations

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  • Niu, Yi-Feng
  • Wan, Xiao-Yu
  • Xu, Xiu-Zhen
  • Ding, Dong

Abstract

Multi-state minimal paths, called d-minimal paths (d-MPs), are a popular tool for computing the reliability of multi-state flow networks. Most of the existing algorithms seek for d-MPs by solving an NP-hard Diophantine system in terms of the implicit enumeration method that is simple yet inefficient. This paper focuses on the development of a novel method for finding all d-MPs. By exploring the relationship between d-MPs and feasible circulations that are a well-known network flow problem, this paper proposes a distinctive method integrating the traditional max-flow algorithm and a partition technique to find all d-MPs. The developed method seeks for d-MPs by solving feasible circulations, rather than by solving an NP-hard Diophantine system; additionally, it neither requires MPs nor generates duplicate d-MPs during the solution process. Both theoretical and experimental results demonstrate the advantage of the developed method, and a real delivery network example is presented to illustrate its application.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:reensy:v:204:y:2020:i:c:s095183202030689x
    DOI: 10.1016/j.ress.2020.107188
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    References listed on IDEAS

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