Hierarchical Cycle-Tree Packing Model for Optimal K-Core Attack

Zhou, Jianwen; Zhou, Hai-Jun

doi:10.1007/s10955-023-03210-7

Cited by 3 publications

(8 citation statements)

References 48 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The last two columns list the mean-field (MF) predictions based on two different models. [30,36] D K hCTGA [34] WN [33] MF [30] MF [36] We see that s(ρ) is a concave function of occupation density ρ. The entropy density approaches zero when ρ reaches the maximum value ρ max = 0.517.…”

Section: Entropy and Maximum Occupation Densitymentioning

confidence: 77%

“…The K-core attack problem is a challenging combinatorial optimization problem. [29][30][31][32][33][34] A special case is the 2-core attack problem (K = 2), which means destroying all the loops in the graph by removing a set of vertices, and it is also known as the feedback vertex set problem. [35,36] In the literature, the practical significance of the feedback vertex set problem has been linked to identifying influential spreaders in a complex network, [37][38][39][40][41] see also review articles.…”

Section: The K-core Attack Problemmentioning

confidence: 99%

“…The other strategy is to map the K-core attack problem to a polymer packing problem. [29,34,36,58] Each polymer is essentially in the shape of a directed tree, with the direction marking the partial time order of the K-core pruning dynamics. Many such polymers are packed together in graph G under some local constraints.…”

Section: The K-core Attack Problemmentioning

confidence: 99%

“…The message-passing algorithms inspired by this implementation are very efficient and are able to construct closeto-minimum K-core attack solutions for single random graph instances. [29,34] Without delving into more technical details, we now review in the following two subsections some main theoretical results obtained on random graphs. Unlike lattice systems, there are no structures in a random graph G. All the edges in such a graph are randomly connected, without any constraint or under the local constraints of fixed vertex degrees.…”

Section: The K-core Attack Problemmentioning

confidence: 99%

“…[36] Table 1. Algorithmic results on the maximum density ρ max of occupied vertices for the K-core attack problem, obtained by the hCTGA [34] and the WN [34] algorithms on regular random graphs of degree D and size N = 10000. The last two columns list the mean-field (MF) predictions based on two different models.…”

Section: Entropy and Maximum Occupation Densitymentioning

confidence: 99%

See 4 more Smart Citations

K-core attack, equilibrium K-core, and kinetically constrained spin system

Zhou 周

2024

Chinese Phys. B

View full text Add to dashboard Cite

Kinetically constrained spin systems are toy models of supercooled liquids and amorphous solids. In this Perspective, we revisit the prototypical Fredrickson-Andersen (FA) kinetically constrained model from the viewpoint of K-core combinatorial optimization. Each kinetic cluster of the FA system, containing all the mutually visitable microscopic occupation configurations, is exactly the solution space of a specific instance of the K-core attack problem. The whole set of different jammed occupation patterns of the FA system is the configuration space of an equilibrium K-core problem. Based on recent theoretical results achieved on the K-core attack and equilibrium K-core problems, we discuss the thermodynamic spin glass phase transitions and the maximum occupation density of the fully unfrozen FA kinetic cluster, and the minimum occupation density and extreme vulnerability of the partially frozen (jammed) kinetic clusters. The equivalence between K-core attack and the fully unfrozen FA kinetic cluster also implies a new way of sampling K-core attack solutions.

show abstract

Section: Entropy and Maximum Occupation Densitymentioning

confidence: 77%

Section: The K-core Attack Problemmentioning

confidence: 99%

Section: The K-core Attack Problemmentioning

confidence: 99%

Section: The K-core Attack Problemmentioning

confidence: 99%

Section: Entropy and Maximum Occupation Densitymentioning

confidence: 99%

See 3 more Smart Citations

K-core attack, equilibrium K-core, and kinetically constrained spin system

Zhou 周

2024

Chinese Phys. B

View full text Add to dashboard Cite

show abstract

Minimum connected dominating set and backbone of a random graph

Habibulla,

Zhou

2024

J. Stat. Mech.

View full text Add to dashboard Cite

We study the minimum dominating set problem as a representative combinatorial optimization challenge with a global topological constraint. The requirement that the backbone induced by the vertices of a dominating set should be a connected subgraph makes the problem rather nontrivial to investigate by statistical physics methods. Here, we convert this global connectivity constraint into a set of local vertex constraints and build a spin glass model with only five coarse-grained vertex states. We derive a set of coarse-grained belief-propagation equations and obtain theoretical predictions of the relative sizes of the minimum dominating sets for regular random and Erdös–Rényi random graph ensembles. We also implement an efficient message-passing algorithm to construct close-to-minimum connected dominating sets and backbone subgraphs for single random graph instances. Our theoretical strategy may also be applicable to some other global topological constraints.

show abstract

Deep Reinforcement Learning for Network Dismantling: A K-Core Based Approach

Pu,

Zeng,

Chen

2024

Mathematics

View full text Add to dashboard Cite

Network dismantling is one of the most challenging problems in complex systems. This problem encompasses a broad array of practical applications. Previous works mainly focus on the metrics such as the number of nodes in the Giant Connected Component (GCC), average pairwise connectivity, etc. This paper introduces a novel metric, the accumulated 2-core size, for assessing network dismantling. Due to the NP-hard computational complexity of this problem, we propose SmartCore, an end-to-end model for minimizing the accumulated 2-core size by leveraging reinforcement learning and graph neural networks. Extensive experiments across synthetic and real-world datasets demonstrate SmartCore’s superiority over existing methods in terms of both accuracy and speed, suggesting that SmartCore should be a better choice for the network dismantling problem in practice.

show abstract

Hierarchical Cycle-Tree Packing Model for Optimal K-Core Attack

Cited by 3 publications

References 48 publications

K-core attack, equilibrium K-core, and kinetically constrained spin system

K-core attack, equilibrium K-core, and kinetically constrained spin system

Minimum connected dominating set and backbone of a random graph

Deep Reinforcement Learning for Network Dismantling: A K-Core Based Approach

Contact Info

Product

Resources

About