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Search for All Minimal Paths in a General Large Flow Network

机译：在一般的大流量网络中搜索所有最小路径

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摘要

An active research field is the evaluation of the reliability of a complex network. The most popular methods for such evaluation often use Minimal Paths (MP) or Minimal Cuts (MC) of the network. Although there are many algorithms developed to search for MP or MC, most of them are inefficient for searching a large network due to the combinatorial explosion problem. Another disadvantage is that the existing algorithms are applicable to specific counts of source and sink nodes (e.g., one-to-one, one-to-many, and so on). This article proposes a novel approach to search for all MP in a general flow network. The term “general” means that the approach can be used to search for all MP with multi-sources, multi-sinks in the network. The edges can be directed, undirected, or hybrid (mixed with directed and undirected arcs). Some benchmarks from the well-known algorithms in the literature are examined and compared. Moreover, the comprehensive tests are also performed with the grid networks, as well as the well-known networks in the literature to show the efficiency of the approach. A sample code is provided in the article for quick validation.
机译：活跃的研究领域是评估复杂网络的可靠性。进行此类评估的最流行方法通常是使用网络的最小路径（MP）或最小切割（MC）。尽管开发了许多搜索MP或MC的算法，但是由于组合爆炸问题，大多数算法在搜索大型网络时效率不高。另一个缺点是现有算法适用于特定数量的源节点和宿节点（例如，一对一，一对多等）。本文提出了一种新颖的方法来搜索通用流网络中的所有MP。术语“通用”表示该方法可用于搜索网络中具有多源，多接收器的所有MP。边缘可以是有向，无向或混合的（与有向和无向弧混合）。研究和比较了文献中一些著名算法的基准。此外，还使用网格网络以及文献中的知名网络进行了综合测试，以显示该方法的效率。本文提供了一个示例代码，用于快速验证。

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