In this paper, we propose a deterministic algorithm that approximates the optimal path cover on weighted undirected graphs. Based on the 1/2-Approximation Path Cover Algorithm by Moran et al., we add a procedure to remove the redundant edges as the algorithm progresses. Our optimized algorithm not only significantly reduces the computation time but also maintains the theoretical guarantee of the original 1/2-Approximation Path Cover Algorithm. To test the time complexity, we conduct numerical tests on graphs with various structures and random weights, from structured ring graphs to random graphs, such as Erdos-Renyi graphs. The tests demonstrate the effectiveness of our proposed algorithm on graphs, especially those with high degree nodes, and the advantages expand as the graph gets larger. Moreover, we also launch tests on various graphs/networks derived from a wide range of real-world problems to suggest the effectiveness and applicability of the proposed algorithm.

翻译：在本文中,我们建议了一种确定性算法,该算法可以与加权非定向图表的最佳路径覆盖相近。根据莫兰等人的1/2-Appractication Path Cover Algorithm,我们添加了一个程序,随着算法的进展,去除多余的边缘。我们优化的算法不仅大大缩短了计算时间,而且还维持了原1/2Appractimation Path Cover Algorithm的理论保证。为了测试时间复杂性,我们用各种结构和随机重量的图表进行数字测试,从结构化环形图到随机图,如Erdos-Renyi图。这些测试显示了我们提议的图表算法的有效性,特别是高节点的图,以及随着图形的扩大而扩大的优势。此外,我们还对从广泛的现实世界问题中得出的各种图表/网络进行了测试,以表明拟议算法的有效性和适用性。