A novel Interpolation technique to address the Edge-Reliability Problem

In this paper we deal with the Edge-Reliability Problem: given a connected simple graph G = (V, E) with perfect nodes and links failing independently with equal probability 1-p, find the probability R_G(p) that the network remains connected. The edge reliability R_G(p) is a polynomial in p with degree m = |E|, and the exact computation of R_G(p) is in the class of NP-Hard problems. However, the related literature is vast, and offers bounds and estimation techniques, as well as exponential algorithms to exactly find that polynomial. We propose a novel interpolation-based technique that exploits the structure of the Hilbert space L²[0; 1], and combines the efficiency of Newton interpolation with the simplicity of Monte Carlo reliability estimation in selected abscissas in [0; 1]. The aim is to guide the polynomial search respecting algebraic properties of the target polynomial coefficients. We illustrate the effectiveness of the algorithm in the lights of a naive graph with limited size, and discuss several hints for future work.