In this paper, the recoverable robust shortest path problem under interval uncertainty representations is discussed. This problem is known to be strongly NP-hard and also hard to approximate in general digraphs. In this paper, the class of acyclic digraphs is considered. It is shown that for the traditional interval uncertainty, the problem can be solved in polynomial time for all natural, known from the literature, neighborhoods. Efficient algorithms for various classes of acyclic digraphs are constructed. Some negative results for general digraphs are strengthened. Finally, some exact and approximate methods of solving the problem under budgeted interval uncertainty are proposed.

翻译：本文探讨了区间不确定性表示下的可恢复鲁棒最短路径问题。该问题已知是强NP困难的，且在一般有向图中也难以近似求解。本文考虑无环有向图类。研究表明，对于传统区间不确定性，该问题可通过多项式时间求解，适用于文献中所有已知的自然邻域结构。针对各类无环有向图，本文构建了高效算法。同时，对一般有向图中的若干负面结果进行了强化。最后，提出了在预算约束区间不确定性下求解该问题的若干精确与近似方法。