This paper presents an algorithm for effectively maintaining the minimum spanning tree in dynamic weighted undirected graphs. The algorithm efficiently updates the minimum spanning tree when the underlying graph structure changes. By identifying the portion of the original tree that can be preserved in the updated tree, our algorithm avoids recalculating the minimum spanning tree from scratch. We provide proof of correctness for the proposed algorithm and analyze its time complexity. In general scenarios, the time complexity of our algorithm is comparable to that of Kruskal’s algorithm. However, the experimental results demonstrate that our algorithm outperforms the approach of recomputing the minimum spanning tree by using Kruskal’s algorithm, especially in medium- and large-scale dynamic graphs where the graph undergoes iterative changes.

Vessel trajectory prediction (VTP) plays a critical role in maritime safety and intelligent navigation. Existing methods struggle to simultaneously capture long-term dependencies and nonlinear dynamic patterns in vessel movements. To address this challenge, we propose MKAIS, a novel trajectory prediction model that integrates the selective state space modeling capability of Mamba with the strong nonlinear representation power of Kolmogorov–Arnold Networks (KAN). Specifically, we design a feature-separated embedding strategy for AIS inputs (longitude, latitude, speed over ground, course over ground), followed by an MKAN module that jointly models global temporal dependencies and nonlinear dynamics. Experiments on the public ct_dma dataset demonstrate that MKAIS outperforms state-of-the-art baselines (LSTM, Transformer, TrAISformer, Mamba), achieving up to 16.65% improvement in the Haversine distance over 3 h prediction horizons. These results highlight the effectiveness and robustness of MKAIS for both short-term and long-term vessel trajectory prediction.

In abstract argumentation frameworks, the computation of stable extensions is an important semantic task for evaluating the acceptability of arguments. The current approaches for the computation of stable extensions are typically conducted through methodologies that are either label-based or extension-based. Label-based algorithms operate by assigning labels to each argument, thus reducing the attack relations between arguments to constraint relations among the labels. This paper analyzes the existing two-label and three-label enumeration algorithms for stable extensions through case studies. It is found that both the two-label and three-label algorithms are not precise enough in defining types of arguments. To address these issues, this paper proposes a four-label enumeration algorithm for stable extensions. This method introduces a$must\_in$ label to pre-mark certain $in$-type arguments, thereby achieving a finer classification of $in$-type arguments. This enhances the labelings’ propagation ability and reduces the algorithm’s search space. Our proposed four-label algorithm was tested on authoritative benchmark sets of abstract argumentation framework problems: ICCMA 2019, ICCMA 2021, and ICCMA 2023. Experimental results show that the four-label algorithm significantly improves solving efficiency compared to existing two-label and three-label algorithms. Additionally, ablation experiments confirm that both the four-label transition strategy and preprocessing strategy enhance the algorithm’s performance.

Argumentation has become one of the important fields of artificial intelligence. This paper proposes a dual-neighborhood tabu search (DNTS) method specifically designed to find a single stable extension in abstract argumentation frameworks. The proposed algorithm implements an improved dual-neighborhood strategy incorporating a fast neighborhood evaluation method. In addition, by introducing techniques such as tabu and perturbation, this algorithm is able to jump out of the local optimum, which significantly improves the performance of the algorithm. In order to evaluate the effectiveness of the method, the performance of the algorithm on more than 300 randomly generated benchmark datasets was studied and compared with the algorithm in the literature. In the experiment, DNTS outperforms the other method regarding time consumption in more than 50 instances and surpasses the other meta-heuristic method in the number of solved cases. Further analysis shows that the initialization method, the tabu strategy, and the perturbation technique help guarantee the efficiency of the proposed DNTS.