An Algebraic Approach to Link Failures Based on Network Coding

In this correspondence, we investigate the link failure problem based on the recent results of network coding. We propose a concept, named capacity factor of a network, which is the minimum link set that can influence the network capacity, as our basic tool. We define the capacity rank to each link of the network to characterize its criticality and present the concept of the p-stable network. Based on these notions, an upper bound for the capacity factor size is derived and a family of p-stable networks is constructed