Node-Reliability
Monte Carlo, Laplace, and Stochastic Approximations and a Greedy Link-Augmentation Strategy
Xinhan Liu (TU Delft - Network Architectures and Services)
Robert Kooij (TNO, TU Delft - Quantum & Computer Engineering)
Piet Van Mieghem (TU Delft - Network Architectures and Services)
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Abstract
The node-reliability polynomial nRelG(p) measures the probability that a connected network remains connected given that each node functions independently with probability p. Computing node-reliability polynomials nRelG(p) exactly is NP-hard. Here we propose efficient approximations. First, we develop an accurate Monte Carlo simulation, which is accelerated by incorporating a Laplace approximation that captures the polynomial’s main behavior. We also introduce three degree-based stochastic approximations (Laplace, arithmetic, and geometric), which leverage the degree distribution to estimate nRelG(p) with low complexity. Beyond approximations, our framework addresses the reliability-based Global Robustness Improvement Problem (k-GRIP) by selecting exactly k links to add to a given graph so as to maximize its node reliability. A Greedy Lowest-Degree Pairing Link Addition (Greedy-LD) Algorithm, is proposed which offers a computationally efficient and practically effective heuristic, particularly suitable for large-scale networks.