The Border Gateway Protocol (BGP) is the core routing protocol for inter-domain routing, providing substantial flexibility but lacking convergence guarantees, which can lead to network oscillations and instability. Despite prior research proposing various methods to address these issues, existing algorithms still fall short in terms of accuracy and efficiency.In this paper, we introduce a novel and efficient algorithm that statically analyzes BGP configurations to accurately determine routing convergence. Our algorithm achieves several major advancements:•Superior Accuracy: It outperforms the state-of-the-art algorithm by correctly identifying a broader range of configurations.•Scalability: It is highly efficient, capable of analyzing Internet-scale configurations within polynomial time complexity.•Reliability: It eliminates false positives, ensuring that potentially oscillating configurations are never incorrectly reported as convergence.Our experimental results demonstrate that the proposed algorithm significantly enhances accuracy and efficiency compared to existing methods, making it highly suitable for large-scale Internet applications. This work represents a substantial step forward in ensuring the stability and reliability of BGP routing, addressing critical challenges in modern Internet infrastructure.

Abstract The Stable Paths Problem (SPP) is a widely adopted model for analyzing the convergence of Border Gateway Protocol (BGP). Solving SPP correctly is of great significance for determining BGP convergence. Existing studies have proposed some SPP solving algorithms that can only solve a part of SPP instances and have limited capabilities. To fill this gap, in this paper we transform SPP into Boolean Satisfiability Problem (SAT) and propose a new SPP solving algorithm called SPPsolver , which can support the solution of any SPP instance. We use Binary Decision Diagrams (BDD) to encode and calculate the SAT formula and apply two optimization methods to accelerate SPPsolver . We use real-world datasets to perform experiments and compare with state-of-the-art algorithms, the results demonstrate the superiority and efficiency of SPPsolver .

Entity alignment (EA) seeks identical entities in different knowledge graphs, which is a long-standing task in the database research. Recent work leverages deep learning to embed entities in vector space and align them via nearest neighbor search. Although embedding-based EA has gained marked success in recent years, it lacks explanations for alignment decisions. In this paper, we present the first framework that can generate explanations for understanding and repairing embedding-based EA results. Given an EA pair produced by an embedding model, we first compare its neighbor entities and relations to build a matching subgraph as a local explanation. We then construct an alignment dependency graph to understand the pair from an abstract perspective. Finally, we repair the pair by resolving three types of alignment conflicts based on dependency graphs. Experiments on a variety of EA datasets demonstrate the effectiveness, generalization, and robustness of our framework in explaining and repairing embedding-based EA results.

Most systems integrating data-driven machine learning with knowledge-driven reasoning usually rely on a specifically designed knowledge base to enable efficient symbolic inference. However, it could be cumbersome for the nonexpert end-users to prepare such a knowledge base in real tasks. Recent years have witnessed the success of large-scale knowledge graphs, which could be ideal domain knowledge resources for real-world machine learning tasks. However, these large-scale knowledge graphs usually contain much information that is irrelevant to a specific learning task. Moreover, they often contain a certain degree of noise. Existing methods can hardly make use of them because the large-scale probabilistic logical inference is usually intractable. To address these problems, we present ABductive Learning with Knowledge Graph (ABL-KG) that can automatically mine logic rules from knowledge graphs during learning, using a knowledge forgetting mechanism for filtering out irrelevant information. Meanwhile, these rules can form a logic program that enables efficient joint optimization of the machine learning model and logic inference within the Abductive Learning (ABL) framework. Experiments on four different tasks show that ABL-KG can automatically extract useful rules from large-scale and noisy knowledge graphs, and significantly improve the performance of machine learning with only a handful of labeled data.

Multi-view data are becoming common in real-world applications and many multi-view clustering algorithms have thus been proposed. The existing algorithms usually focus on the cooperation of different visible views in the original space but neglect the influence of the hidden information among these visible views, or they only consider the hidden information among the views. The algorithms are therefore not efficient since the available information is not fully exploited, particularly the otherness information in different views and the consistency information among them. In practice, the otherness and consistency information in multi-view data are both very useful for effective clustering analyses. In this study, a Multi-View clustering algorithm with the Cooperation of Visible and Hidden views, i.e., MV-Co-VH, is proposed. The MV-Co-VH algorithm first projects the multiple views from different visible spaces to the common hidden space by using non-negative matrix factorization to obtain the common hidden view data. Collaborative learning is then implemented in the clustering procedure based on the visible views and the shared hidden view. The experimental results of extensive experiments on UCI multi-view datasets and real-world image multi-view datasets show that the clustering performance of the proposed algorithm is competitive with or even better than that of the existing algorithms.