  We consider a cyber-physical system consisting of two interacting networks,
i.e., a cyber-network overlaying a physical-network. It is envisioned that
these systems are more vulnerable to attacks since node failures in one network
may result in (due to the interdependence) failures in the other network,
causing a cascade of failures that would potentially lead to the collapse of
the entire infrastructure. The robustness of interdependent systems against
this sort of catastrophic failure hinges heavily on the allocation of the
(interconnecting) links that connect nodes in one network to nodes in the other
network. In this paper, we characterize the optimum inter-link allocation
strategy against random attacks in the case where the topology of each
individual network is unknown. In particular, we analyze the "regular"
allocation strategy that allots exactly the same number of bi-directional
inter-network links to all nodes in the system. We show, both analytically and
experimentally, that this strategy yields better performance (from a network
resilience perspective) compared to all possible strategies, including
strategies using random allocation, unidirectional inter-links, etc.
