Principled Network Reliability Approximation: A Counting-Based Approach

TL;DR

This paper reviews classical and modern methods for network reliability approximation, introducing K-RelNet, a counting-based estimator that provides PAC-guarantees for the K-terminal reliability problem, supported by benchmark testing.

Contribution

It introduces K-RelNet, a novel counting-based approach that offers PAC-guaranteed approximations for network reliability, advancing scalable and reliable estimation techniques.

Findings

K-RelNet delivers PAC-guaranteed estimates.

Benchmark tests show competitive performance.

Methods span from classical to modern techniques.

Abstract

As engineered systems expand, become more interdependent, and operate in real-time, reliability assessment is indispensable to support investment and decision making. However, network reliability problems are known to be #P-complete, a computational complexity class largely believed to be intractable. The computational intractability of network reliability motivates our quest for reliable approximations. Based on their theoretical foundations, available methods can be grouped as follows: (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, as it harbors computationally feasible approximation schemes with PAC-guarantees. We give a comprehensive review of classical methods before introducing modern techniques and our developments. We introduce K-RelNet, an extended counting-based estimation method that delivers PAC-guarantees for the K-terminal reliability problem. Then, we test methods' performance using various benchmark systems. We highlight the range of application of algorithms and provide the foundation for future resilience engineering as it increasingly necessitates methods for uncertainty quantification in complex systems.