# A Graph Convolutional Network-Based Method for Congested Link Identification
###### Abstract
Network Boolean tomography is a generalization of network tomography technology to the realm of Boolean algebra [13]. Boolean network tomography uses \"0\" and \"1\" to indicate whether a link or path in a network is congested. A link is labeled as \"1\" if it is congested and \"0\" if it is not. The congestion state of a path is related to the state of the links it traverses. The relation between path status and link status can be represented by the logical operator \"OR\". In other words, a path is good if all links it traverses are good; otherwise, it is congested if at least one of the links it traverses is congested. Identification of congested links is crucial for adjusting routing policies and controlling congestion. Based on the relationship between end-to-end path congestion and link congestion, it is possible to construct multiple equations from the path states, which are obtained through the operation or computation of all links traversed by the paths. However, since the number of links in the network is typically larger than the number of paths, the feasible solution to this problem is not unique. For instance, consider the scenario depicted in Figure 1, where four terminal nodes (\(d_{1}\), \(d_{2}\), \(d_{3}\), and \(d_{4}\)) gather data and converge to a base station \(s\) via a WSN. If the paths from \(d_{2}\), \(d_{3}\), and \(d_{4}\) to the base station \(s\) are congested, then we cannot solve for an exact result, except for the link between \(d_{1}\) and an inner node \(e_{1}\). In such scenarios, by leveraging the network's topology and fundamental performance parameters, collected end-to-end network measurements serve as valuable sample data to estimate the probability distribution of performance parameters. This statistical approach offers a nuanced understanding of various network conditions, particularly regarding congestion. By extrapolating insights from this analysis, informed decisions can be made to manage and optimize network performance without the necessity of expanding the monitoring infrastructure. Network tomography has garnered significant attention due to its ability to reduce monitoring overhead in a network by inferring unknown internal link states based solely on end-to-end measurements. Numerous studies have explored its application in various network scenarios. For instance, in [14], a solution is presented for inferring the network topology, while [15] focused on loss rate inference by selecting a minimal set of paths. Recently, the authors of [16] introduced the incorporation of path information to infer link metrics. Additionally, research has investigated network tomography's robustness under failure [17] and explored the security vulnerabilities associated with these approaches [18]. A recent survey comprehensively discussed the state of the art in network tomography [19]. Furthermore, recent advancements in this field have leveraged machine learning (ML) techniques to estimate the additive metrics of network slices, such as delays or logarithms of loss rates. In particular, the authors of [20] employed neural networks to address this challenge, demonstrating the potential of ML in enhancing network tomography. Meanwhile, the authors of [21] focused specifically on the intricacies posed by unknown links and dynamic routing, offering innovative solutions to overcome these issues within the context of network tomography. Network Boolean tomography, as an extension of network tomography technology to Boolean algebra, has garnered extensive attention for its inherent advantages in computational complexity reduction and data processing efficiency enhancement. [PERSON] et al. [22] proposed the CLINK algorithm, which introduces the probability model into congested link inference. Moreover, through multi-slot path performance detection, it effectively avoids the strong dependence of single-slot path detection on clock synchronization [23].