  The giant mutually connected component (GMCC) of an interdependent or
multiplex network collapses with a discontinuous hybrid transition under random
damage to the network. If the nodes to be damaged are selected in a targeted
way, the collapse of the GMCC may occur significantly sooner. Finding the
minimal damage set which destroys the largest mutually connected component of a
given interdependent network is a computationally prohibitive simultaneous
optimization problem. We introduce a simple heuristic strategy -- Effective
Multiplex Degree -- for targeted attack on interdependent networks that
leverages the indirect damage inherent in multiplex networks to achieve a
damage set smaller than that found by any other non computationally intensive
algorithm. We show that the intuition from single layer networks that decycling
(damage of the $2$-core) is the most effective way to destroy the giant
component, does not carry over to interdependent networks, and in fact such
approaches are worse than simply removing the highest degree nodes.
