Search for All Minimal Paths in a General Large Flow Network

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.

Acronyms MC/MP

Minimal Cut/Minimal Path

LBP/UBP

Lower Boundary Point/Upper Boundary Point

DFS

Depth-First Search