Large-scale power blackouts caused by cascading failure are inflicting enormous socioeconomic costs. We study the problem of cascading link failures in power networks modelled by random geometric graphs from a percolation-based viewpoint. To reflect the fact that links fail according to the amount of power flow going through them, we introduce a model where links fail according to a probability which depends on the number of neighboring links. We devise a mapping which maps links in a random geometric graph to nodes in a corresponding dual covering graph. This mapping enables us to obtain the firstknown analytical conditions on the existence and non-existence of a large component of operational links after degree-dependent link failures. Next, we present a simple but descriptive model for cascading link failure, and use the degree-dependent link failure results to obtain the first-known analytical conditions on the existence and non-existence of cascading link failures.

As organizations and individuals have begun to rely more and more heavily on cloud-service providers for critical tasks, cloud-service reliability has become a top priority. It is natural for cloud-service providers to use redundancy to achieve reliability. For example, a provider may replicate critical state in two data centers. If the two data centers use the same power supply, however, then a power outage will cause them to fail simultaneously; replication per se does not, therefore, enable the cloud-service provider to make strong reliability guarantees to its users. Zhai et al.[28] present a system, which they refer to as a structural-reliability auditor (SRA), that uncovers common dependencies in seemingly disjoint cloudinfrastructural components (such as the power supply in the example above) and quantifies the risks that they pose. In this paper, we focus on the need for structural-reliability auditing to be done in a privacy-preserving manner. We present a privacy-preserving structural-reliability auditor (P-SRA), discuss its privacy properties, and evaluate a prototype implementation built on the Sharemind SecreC platform [6]. P-SRA is an interesting application of secure multi-party computation (SMPC), which has not often been used for graph problems. It can achieve acceptable running times even on large cloud structures by using a novel data-partitioning technique that may be useful in other applications of SMPC.

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