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.

9 pages, 9 figures