Decycling and dismantling of complex networks are underlying many important
applications in network science. Recently these two closely related problems
were tackled by several heuristic algorithms, simple and considerably
sub-optimal, on the one hand, and time-consuming message-passing ones that
evaluate single-node marginal probabilities, on the other hand. In this paper
we propose a simple and extremely fast algorithm, CoreHD, which recursively
removes nodes of the highest degree from the 2-core of the network. CoreHD
performs much better than all existing simple algorithms. When applied on
real-world networks, it achieves equally good solutions as those obtained by
the state-of-art iterative message-passing algorithms at greatly reduced
computational cost, suggesting that CoreHD should be the algorithm of choice
for many practical purposes
