Enumerating circular disk failures covering a single node

Current backbone networks are designed to protect a certain pre-defined list of failures, called Shared Risk Link Groups (SRLG). The list of SRLGs must be defined carefully, because leaving out one likely failure event significantly degrades the observed reliability of the network. In practice, the list of SRLGs is typically composed of every single link or node failure. It has been observed that some type of failure events manifested at multiple locations of the network, which are physically close to each other. Such failure events are called regional failures, and are often caused by a natural disaster. A common belief is that the number of possible regional failures can be large, thus simply listing them as SRLGs is not a viable solution. In this study we show the opposite, and provide an efficient algorithm enumerating all the regional failures having at a node failed as SRLGs. According to some practical assumptions this list is surprisingly short with O(|V|) SRLGs in total, and can be computed in O(|V|2) time.