In the problem, we look for an -path that is at least vertices longer than a shortest one. We study the parameterized complexity of when parameterized by : this falls into the research paradigm of ‘parameterization above guarantee’. Whereas the problem is known to be fixed-parameter tractable (FPT) on undirected graphs, the status of on directed graphs remains highly unclear: it is not even known to be solvable in polynomial time for . Recently, Fomin et al. made progress in this direction by showing that the problem is FPT on every class of directed graphs where the problem is solvable in polynomial time. We improve upon their result by weakening this assumption: we show that only a polynomial-time algorithm for is required.

中文翻译：

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长定向绕路：减少 2 条不相交路径

在该问题中，我们寻找一条至少比最短顶点长的路径。我们研究参数化时的参数化复杂度：这属于“参数化高于保证”的研究范式。尽管已知该问题在无向图上是固定参数可处理（FPT）的，但有向图上的状态仍然非常不清楚：甚至不知道它是否可以在多项式时间内解决。最近，福明等人。通过证明该问题在每类有向图上都是 FPT，其中该问题可以在多项式时间内解决，从而在这个方向上取得了进展。我们通过削弱这个假设来改进他们的结果：我们证明只需要多项式时间算法。