Detecting critical nodes in sparse graphs is important in a variety of application domains, such as network vulnerability assessment, epidemic control, and drug design. The 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. Computational 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.

翻译：检测稀疏图中的关键节点在多个应用领域具有重要意义，例如网络脆弱性评估、疫情控制和药物设计。关键节点问题（CNP）旨在从网络中找出一个节点集合，删除这些节点后能最大程度地降低剩余网络的成对连通性。由于该问题通常具有NP难性质，当前最先进的CNP解决方案主要基于启发式方法。这类方法的设计通常需要领域知识和反复试验，耗时耗力。本文首次提出一种特征重要性感知的图注意力网络用于节点表示，并将其与决斗双深度Q网络相结合，构建了一种端到端算法来解决CNP。该算法无需大多数现有方法所需的特定领域知识或标注数据集。模型训练完成后，无需重新训练即可推广应用于不同类型的CNP（具有不同规模和拓扑结构）。在28个真实网络上的计算实验表明，所提方法与现有最优方法高度可比。由于无需任何特定领域知识，该方法可适用于包括现有方法无法处理的众多应用场景。进一步结合局部搜索方法可提升其求解质量。广泛的对比结果验证了其在求解CNP上的有效性。