@article{dimuro2015recovery,
author = "M. A. {Di Muro} and C. E. {La Rocca} and H. E. Stanley and S. Havlin and L. A. Braunstein",
abstract = "Recent network research has focused on the cascading failures in a system of interdependent networks and the necessary preconditions for system collapse. An important question that has not been addressed is how to repair a failing system before it suffers total breakdown. Here we introduce a recovery strategy of nodes and develop an analytic and numerical framework for studying the concurrent failure and recovery of a system of interdependent networks based on an efficient and practically reasonable strategy. Our strategy consists of repairing a fraction of failed nodes, with probability of recovery {\$}\backslashgamma{\$}, that are neighbors of the largest connected component of each constituent network. We find that, for a given initial failure of a fraction {\$}1-p{\$} of nodes, there is a critical probability of recovery above which the cascade is halted and the system fully restores to its initial state and below which the system abruptly collapses. As a consequence we find in the plane {\$}\backslashgamma-p{\$} of the phase diagram three distinct phases. A phase in which the system never collapses without being restored, another phase in which the recovery strategy avoids the breakdown, and a phase in which even the repairing process cannot avoid the system collapse.",
doi = "10.1038/srep22834",
isbn = "doi:10.1038/srep22834",
issn = "2045-2322",
journal = "Scientific Reports",
number = "7600",
pages = "22834",
publisher = "Nature Publishing Group",
title = "{R}ecovery of {I}nterdependent {N}etworks",
url = "http://arxiv.org/abs/1512.02555",
volume = "6",
year = "2015",
}