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Lower bound of network dismantling problem.

Jiachen Sun1, Rong Liu2, Zhengping Fan2

  • 1School of Electronics and Information Technology, Sun Yat-sen University, Guangzhou 510006, China.

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Summary
This summary is machine-generated.

Finding the smallest set of nodes to break a network is computationally hard. This study proposes a new method using subnetworks to find better lower bounds for network dismantling, improving heuristic algorithm evaluation.

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Area of Science:

  • Network Science
  • Graph Theory
  • Computational Complexity

Background:

  • The network dismantling problem seeks the minimum nodes to remove for network fragmentation.
  • Identifying this minimum set is an NP-hard problem, making exact solutions infeasible for large networks.
  • Accurate lower bounds are crucial for evaluating heuristic algorithms that approximate the dismantling set.

Purpose of the Study:

  • To develop a more effective method for determining lower bounds of dismantling sets in complex networks.
  • To improve the evaluation of heuristic algorithms for the network dismantling problem.
  • To leverage network properties for enhanced lower bound estimation.

Main Methods:

  • Utilizing heterogeneous degree distribution properties of networks.
  • Applying 2-core decomposition to identify network structures.
  • Calculating lower bounds on subnetworks derived from the original network.
  • Comparing lower bound performance on original versus modified network structures.

Main Results:

  • A novel approach for calculating lower bounds of dismantling sets is presented.
  • The proposed method, focusing on subnetworks, yields significantly better lower bounds than direct application to the original network.
  • This improvement is particularly pronounced in real-world network structures.
  • The effectiveness is linked to strategic prior removal of specific nodes.

Conclusions:

  • Lower bound estimation for network dismantling can be substantially improved by analyzing carefully selected subnetworks.
  • The method provides a more rigorous benchmark for assessing the performance of heuristic network dismantling algorithms.
  • This research offers a valuable tool for understanding network resilience and robustness.