title: Cascading failures in networks with proximate dependent nodes.
abstract: We study the mutual percolation of a system composed of two interdependent random regular networks. We introduce a notion of distance to explore the effects of the proximity of interdependent nodes on the cascade of failures after an initial attack. We find a nontrivial relation between the nature of the transition through which the networks disintegrate and the parameters of the system, which are the degree of the nodes and the maximum distance between interdependent nodes. We explain this relation by solving the problem analytically for the relevant set of cases. In the process, we solve a variant of Rényi's parking problem on treelike graphs.
authors.affiliation: Department of Physics, Yeshiva University, 500 West 185th Street, New York, New York 10033, USA.
authors.forename: Yosef
authors.initials: Y
authors.lastname: Kornbluth
authors.affiliation: Department of Physics, Yeshiva University, 500 West 185th Street, New York, New York 10033, USA.
authors.forename: Steven
authors.initials: S
authors.lastname: Lowinger
authors.affiliation: Department of Physics, Yeshiva University, 500 West 185th Street, New York, New York 10033, USA.
authors.forename: Gabriel
authors.initials: G
authors.lastname: Cwilich
authors.affiliation: Department of Physics, Yeshiva University, 500 West 185th Street, New York, New York 10033, USA.
authors.forename: Sergey V
authors.initials: SV
authors.lastname: Buldyrev