  Various networks are broadly and deeply applied in real-life applications.
Reliability is the most important index for measuring the performance of all
network types. Among the various algorithms, only implicit enumeration
algorithms, such as depth-first-search, breadth-search-first, universal
generating function methodology, binary-decision diagram, and
binary-addition-tree algorithm (BAT), can be used to calculate the exact
network reliability. However, implicit enumeration algorithms can only be used
to solve small-scale network reliability problems. The BAT was recently
proposed as a simple, fast, easy-to-code, and flexible make-to-fit
exact-solution algorithm. Based on the experimental results, the BAT and its
variants outperformed other implicit enumeration algorithms. Hence, to overcome
the above-mentioned obstacle as a result of the size problem, a new parallel
BAT (PBAT) was proposed to improve the BAT based on compute multithread
architecture to calculate the binary-state network reliability problem, which
is fundamental for all types of network reliability problems. From the analysis
of the time complexity and experiments conducted on 20 benchmarks of
binary-state network reliability problems, PBAT was able to efficiently solve
medium-scale network reliability problems.
