We introduce a novel approach of using important cuts which allowed us to design significantly faster fixed-parameter tractable (FPT) algorithms for the following routing problems: the Mixed Chinese Postman Problem parameterized by the number of directed edges (Gutin et al., JCSS 2017), the Minimum Shared Edges problem (MSE) parameterized by the number p of paths between two specified vertices (Fluschnik et al., JCSS 2019), and the Weighted Min Cut Prevention problem (Gruttemeier et al., WG 2021). The Minimum Vulnerability problem (MV) is a generalization of MSE (Assadi et al., Algorithmica 2014). The only known FPT algorithm for MV parameterized by p (the same parameter as for MSE) was for chordal graphs (Aoki et al., JCO 2018). We design an FPT algorithm for MV on all undirected graphs.
翻译:我们引入了一种新颖的方法,使用重要的削减方法,从而使我们能够为以下路由问题设计出大大加快的固定参数可移动算法(FPT):由定向边缘数(Gutin等人,2017年,JCSS2017年)组成的混合中国邮差问题参数;由两个指定的脊椎间路径数(Fluschnik等人,JCSS2019年)和轻度中截面预防问题(Gruttemeier等人,WG2021年);最低易变性问题(MV)是MSE(Asadi等人,Algorithmica,2014年)的概括化。由p(MSE的参数与MSE的参数相同)组成的最低共享边缘参数参数(MSE)中唯一已知的MV参数(FPT算法)是用于圆形图(Aoki等人,JCO 2018年)之间的路径数(Aoki等人,JCO2018年)。我们为所有未定向图形的MV设计了FP算法。