Enhancing Computational Efficiency of Network Reliability with a New Prime Shortest Path Algorithm

To address the increasing demands of modern networks, evaluating computational efficiency of modified network reliability is essential, with minimal paths (MPs) serving as a critical factor. However, traditional approaches to assessing computational efficiency of network reliability often struggle with challenges such as duplicate MPs and sub-path identification, resulting in exponential computational time. In this study, we present a novel algorithm based on the Prime Shortest Path (PSP) approach, which efficiently resolves these challenges by self-detecting and eliminating duplication in polynomial time. This marks a significant improvement over existing methods. The algorithm’s correctness is rigorously validated, and its superior performance is confirmed through a detailed time complexity analysis and comparisons with the leading state-of-the-art algorithms.