Matchings and T-joins are fundamental and much-studied concepts in graph theory and combinatorial optimization. One important application of matchings and T-joins is in the computation of strong lower bounds for arc routing problems (ARPs). An ARP is a special kind of vehicle routing problem, in which the demands are located along edges or arcs, rather than at nodes. We point out that the literature on applying matchings and T-joins to ARPs does not fully exploit the structure of real-life road networks. We propose some ways to exploit this structure. Computational results show significant running time improvements, without deteriorating the quality of the lower bounds.

中文翻译：

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道路网络中的匹配、T 型连接和弧形布线

匹配问题和牛逼-加入是图论与组合优化基本和研究较多的概念。匹配和T连接的一项重要应用是计算弧路由问题(ARP)的强下界。ARP 是一种特殊的车辆路径问题，其中需求位于边或弧上，而不是位于节点处。我们指出，将匹配和T连接应用于 ARP的文献并没有充分利用现实道路网络的结构。我们提出了一些利用这种结构的方法。计算结果显示运行时间显着改善，而不会降低下界的质量。