Dual-failure distance and connectivity oracles

Spontaneous failure is an unavoidable aspect of all networks, particularly those with a physical basis such as communications networks or road networks. Whether due to malicious coordinated attacks or other causes, failures temporarily change the topology of the network and, as a consequence, its connectivity and distance metric. In this paper we look at the problem of efficiently answering connectivity, distance, and shortest route queries in the presence of two node or link failures. Our data structure uses O(n2) space and answers queries in O (1) time, which is within a polylogarithmic factor of optimal and nearly matches the single-failure distance oracles of Demestrescu et al. It may yet be possible to find distance/connectivity oracles capable of handling any fixed number of failures. However, the sheer complexity of our algorithm suggests that moving beyond dual-failures will require a fundamentally different approach to the problem.