Feature Importance-aware Graph Attention Network and Dueling Double Deep Q-Network Combined Approach for Critical Node Detection Problems

Detecting critical nodes in sparse networks is important in a variety of application domains. A Critical Node Problem (CNP) aims to find a set of critical nodes from a network whose deletion maximally degrades the pairwise connectivity of the residual network. Due to its general NP-hard nature, state-of-the-art CNP solutions are based on heuristic approaches. Domain knowledge and trial-and-error are usually required when designing such approaches, thus consuming considerable effort and time. This work proposes a feature importance-aware graph attention network for node representation and combines it with dueling double deep Q-network to create an end-to-end algorithm to solve CNP for the first time. It does not need any problem-specific knowledge or labeled datasets as required by most of existing methods. Once the model is trained, it can be generalized to cope with various types of CNPs (with different sizes and topological structures) without re-training. Extensive experiments on 28 real-world networks show that the proposed method is highly comparable to state-of-the-art methods. It does not require any problem-specific knowledge and, hence, can be applicable to many applications including those impossible ones by using the existing approaches. It can be combined with some local search methods to further improve its solution quality. Extensive comparison results are given to show its effectiveness in solving CNP.