Abstract
Understanding and improving the robustness of networks has significant applications in various areas, such as bioinformatics, transportation, critical infrastructures, and social networks. Recently, there has been a large amount of work on network dismantling, which focuses on removing an optimal set of nodes to break the network into small components with sub-extensive sizes. However, in our experiments, we found these state-of-the-art methods, although seemingly different, utilize the same refinement technique, namely reinsertion, to improve the performance. Despite being mentioned with understatement, the technique essentially plays the key role in the final performance. Without reinsertion, the current best method would deteriorate worse than the simplest heuristic ones; while with reinsertion, even the random removal strategy achieves on par with the best results. As a consequence, we, for the first time, systematically revisit the power of reinsertion in network dismantling problems. We re-implemented and compared 10 heuristic and approximate competing methods on both synthetic networks generated by four classical network models, and 18 real-world networks which cover seven different domains with varying scales. The comprehensive ablation results show that: i) HBA (High Betweenness Adaption, no reinsertion) is the most effective network dismantling strategy, however, it can only be applicable in small scale networks; ii) HDA (High Degree Adaption, with reinsertion) achieves the best balance between effectiveness and efficiency; iii) The reinsertion techniques help improve the performance for most current methods; iv) The one, which adds back the node based on that it joins the clusters minimizing the multiply of both numbers and sizes, is the most effective reinsertion strategy for most methods. Our results can be a survey reference to help further understand the current methods and thereafter design the better ones.
Highlights
Many real-world systems can be described through the complex network perspective, including air transport [17], power grid [3], malicious organization [9, 10], Internet [3] or inter-personal networks [15]
We systematically investigate the power of reinsertion on the current methods for network dismantling
Results we first demonstrate the effectiveness of the reinsertion technique on both synthetic graphs and real-world networks, we explore the effects of different reinsertion techniques
Summary
Many real-world systems can be described through the complex network perspective, including air transport [17], power grid [3], malicious organization [9, 10], Internet [3] or inter-personal networks [15]. The exact solution is computationally intractable for medium and large networks due to its NP-hard nature [5], a large number of approximate methods have been proposed, including the heuristic methods [4, 11, 12, 21, 23, 31], and some message-passing algorithms [5, 22] The former methods often greedily (2020) 9:24 select target nodes based on local metrics, like node degree, which often leads to sub-optimal solutions; the latter ones are more accurate and global, while they need to iterate certain steps on the whole network to select the suitable candidate nodes [31], which would sacrifice some efficiency. Such confused results prevent us from selecting the best algorithm to handle the application at hand
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