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We consider network reliability in layered networks where the lower layer experiences random link failures. In layered networks, each failure at the lower layer may lead to multiple failures at the upper layer. We generalize the classical polynomial expression for network reliability to the multi-layer setting. Using random sampling techniques, we develop polynomial time approximation algorithms for the failure polynomial. Our approach gives an approximate expression for reliability as adoi:10.1109/tnet.2011.2143425 fatcat:t7atomfzrrdo5lf7mwcto4vfse