Bounds evaluation of coefficients in the reliability polynomial

In this study a class of new methods to evaluate bounds of the reliability polynomial coefficients is proposed. These new methods enumerate progressively simple paths or p-acyclic subgraphs finding for each new term a closer lower bound. The process, for high complex networks, can be interrupted, obtaining in this case only approximate values, while the final exact results can be obtained for computationally tractable networks. Alternatively, the a priori knowledge of all simple paths allows us to find a succession of upper and lower bounds still convergent to the exact values of coefficients. Finally, a comparison is done between the results obtained in this paper and those already presented in the literature.