Self Healing Percolation

We discuss a simple model of self-healing for complex networks; in particular, self-healing capabilities are implemented through distributed communication protocols that exploit redundant links to recover the connectivity of the system. We analyse the effect of the level of redundancy on the resilience to multiple failures measured as the fraction of nodes still served after network damages. We then study the effects of redundancy under different connectivity patterns -- from planar grids, to small-world, up to scale-free networks -- on healing performances. Finally, we first discuss some recent analytical results for square grids and Erdos-Renyi graphs and then introduce a cavity approach to study the recovery of connectivity after damage in self-healing networks.