  Interdependencies are ubiquitous throughout the world. Every real-world
system interacts with and is dependent on other systems, and this
interdependency affects their performance. In particular, interdependencies
among networks make them vulnerable to failure cascades, the effects of which
are often catastrophic. Failure propagation fragments network components,
disconnects them, and may cause complete systemic failure. We propose a
strategy of avoiding or at least mitigating the complete destruction of a
system of interdependent networks experiencing a failure cascade. Starting with
a fraction $1-p$ of failing nodes in one network, we reconnect with a
probability $\gamma$ every isolated component to a functional giant component
(GC), the largest connected cluster. We find that as $\gamma$ increases the
resilience of the system to cascading failure also increases. We also find that
our strategy is more effective when it is applied in a network of low average
degree. We solve the problem theoretically using percolation theory, and we
find that the solution agrees with simulation results.
