  The overwhelming majority of survivable (fault-tolerant) network design
models assume a uniform scenario set. Such a scenario set assumes that every
subset of the network resources (edges or vertices) of a given cardinality $k$
comprises a scenario. While this approach yields problems with clean
combinatorial structure and good algorithms, it often fails to capture the true
nature of the scenario set coming from applications.
  One natural refinement of the uniform model is obtained by partitioning the
set of resources into faulty and secure resources. The scenario set contains
every subset of at most $k$ faulty resources. This work studies the
Fault-Tolerant Path (FTP) problem, the counterpart of the Shortest Path problem
in this failure model. We present complexity results alongside exact and
approximation algorithms for FTP. We emphasize the vast increase in the
complexity of the problem with respect to its uniform analogue, the
Edge-Disjoint Paths problem.

Data Structures and Algorithms;Optimization and Control