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