Detecting Critical Nodes in Sparse Graphs via “Reduce-Solve-Combine” Memetic Search

Abstract

This study considers a well-known critical node detection problem that aims to minimize a pairwise connectivity measure of an undirected graph via the removal of a subset of nodes (referred to as critical nodes) subject to a cardinality constraint. Potential applications include epidemic control, emergency response, vulnerability assessment, carbon emission monitoring, network security, and drug design. To solve the problem, we present a “reduce-solve-combine” memetic search approach that integrates a problem reduction mechanism into the popular population-based memetic algorithm framework. At each generation, a common pattern mined from two parent solutions is first used to reduce the given problem instance, then the reduced instance is solved by a component-based hybrid neighborhood search that effectively combines an articulation point impact strategy and a node weighting strategy, and finally an offspring solution is produced by combining the mined common pattern and the solution of the reduced instance. Extensive evaluations on 42 real-world and synthetic benchmark instances show the efficacy of the proposed method, which discovers nine new upper bounds and significantly outperforms the current state-of-the-art algorithms. Investigation of key algorithmic modules additionally discloses the importance of the proposed ideas and strategies. Finally, we demonstrate the generality of the proposed method via its adaptation to solve the node-weighted critical node problem. History: Accepted by Erwin Pesch, Area Editor for Heuristic Search & Approximation Algorithms. Funding: This work was supported by the National Natural Science Foundation of China [Grants 72371157, 61903144, 72031007]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0130 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0130 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .