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。该问题在一般有向图中被证明是强NP难且难以近似的。本文针对无环有向图类进行研究。结果表明，对于传统的区间不确定性，该问题在文献中已知的所有自然邻域内均可在多项式时间内求解。本文为各类无环有向图构建了高效算法，同时加强了一般有向图中的若干否定性结论。最后，针对预算区间不确定性下的该问题，提出了若干精确与近似求解方法。