Cycle-tree guided attack of random K-core: Spin glass model and efficient message-passing algorithm

The K-core of a graph is the maximal subgraph within which each vertex connected to at least K other vertices. It fundamental network concept for understanding threshold cascading processes with discontinuous percolation transition. A minimum attack set contains smallest number vertices whose removal induces complete collapse K-core. Here we tackle this prototypical optimal initial-condition problem from spin-glass perspective cycle-tree maximum packing and propose guided (CTGA) message-passing algorithm. good performance time efficiency CTGA are verified on regular random Erdös-Rényi ensembles. Our central idea transforming long-range correlated dynamical process static structural patterns may also be instructive hard optimization control problems.