Robustness estimation is critical for the design and maintenance of resilient networks, one of the global challenges of the 21st century. Existing studies exploit network metrics to generate attack strategies, which simulate intentional attacks in a network, and compute a metric-induced robustness estimation. While some metrics are easy to compute, e.g. degree centrality, other, more accurate, metrics require considerable computation efforts, e.g. betweennes centrality. We propose a new algorithm for estimating the robustness of a network in sub-quadratic time, i.e., significantly faster than betweenness centrality. Experiments on real-world networks and random networks show that our algorithm estimates the robustness of networks close to or even better than betweenness centrality, while being orders of magnitudes faster. Our work contributes towards scalable, yet accurate methods for robustness estimation of large complex networks.