Principled network reliability approximation: A counting-based approach

As engineered systems expand, become more interdependent, and operate in real-time, reliability assessment is key to inform investment and decision making. However, network reliability problems are known to be #P-complete, a computational complexity class believed to be intractable, and thus motivate the quest for approximations. Based on their theoretical foundations, reliability evaluation methods can be grouped as: (i) exact or bounds, (ii) guarantee-less sampling, and (iii) probably approximately correct (PAC). Group (i) is well regarded due to its useful byproducts, but it does not scale in practice. Group (ii) scales well and verifies desirable properties, such as the bounded relative error, but it lacks error guarantees. Group (iii) is of great interest when precision and scalability are required. We introduce K-RelNet, an extended counting-based method that delivers PAC guarantees for the K-terminal reliability problem. We also put our developments in context relative to classical and emerging techniques to facilitate dissemination. Then, we test in a fair way the performance of competitive methods using various benchmark systems. We note the range of application of algorithms and suggest a foundation for future computational reliability and resilience engineering, given the need for principled uncertainty quantification across complex networked systems.