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

• URL: http://arxiv.org/abs/2110.05940v3
• Date: Tue, 19 Jul 2022 06:05:31 GMT
• Title: Cycle-tree guided attack of random K-core: Spin glass model and efficient message-passing algorithm
• Authors: Hai-Jun Zhou
• Abstract summary: A minimum attack set contains the smallest number of vertices whose removal induces complete collapse of the K-core. Here we tackle this optimal initial-condition problem from the spin-glass perspective of cycle-tree maximum packing. The good performance and time efficiency of CTGA are verified on the regular random and Erd"os-R'enyi random graph ensembles.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 spin-glass 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 Erd\"os-R\'enyi random graph ensembles. Our central idea of transforming 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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