Sampling and active learning methods for network reliability estimation using K-terminal spanning tree

TL;DR

This work tackles the challenge of scalable two-terminal network reliability estimation under node and edge failures by introducing a Monte Carlo method built on a K-terminal spanning tree (MC-KST) and an active-learning extension (AL-KST) that employs a random-forest surrogate to generalize across topologies. The MC-KST method leverages the K-terminal spanning tree to compute multiple structure-function values per lifetime sample, enabling efficient survival-signature estimation, while a transformation maps node failures to an edge-failure framework. The AL-KST method augments MC-KST with iterative RF-based learning, selective sampling via entropy, and a stopping rule to adapt to variant networks with significantly reduced computational effort. Across six synthetic networks and two real-world cases, both methods achieve high accuracy, with AL-KST offering substantial efficiency gains and adaptability, though RF-based approaches may struggle with large-scale imbalance; the results underscore practical utility for reliability assessment in complex infrastructure networks.

Abstract

Network reliability analysis remains a challenge due to the increasing size and complexity of networks. This paper presents a novel sampling method and an active learning method for efficient and accurate network reliability estimation under node failure and edge failure scenarios. The proposed sampling method adopts Monte Carlo technique to sample component lifetimes and the K-terminal spanning tree algorithm to accelerate structure function computation. Unlike existing methods that compute only one structure function value per sample, our method generates multiple component state vectors and corresponding structure function values from each sample. Network reliability is estimated based on survival signatures derived from these values. A transformation technique extends this method to handle both node failure and edge failure. To enhance efficiency of proposed sampling method and achieve adaptability to network topology changes, we introduce an active learning method utilizing a random forest (RF) classifier. This classifier directly predicts structure function values, integrates network behaviors across diverse topologies, and undergoes iterative refinement to enhance predictive accuracy. Importantly, the trained RF classifier can directly predict reliability for variant networks, a capability beyond the sampling method alone. Through investigating several network examples and two practical applications, the effectiveness of both proposed methods is demonstrated.

Figures (21)

• Figure 1: Basic procedure of K-terminal spanning tree algorithm
• Figure 2: Description of structure function values and survival signature samples generated by the proposed MC-KST method
• Figure 3: Flowchart of the proposed MC-KST method
• Figure 4: Illustration of equivalent transforming node failure problem to edge failure problem
• Figure 5: Illustration of random forest classifier