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：[译文摘要] 本文探讨了区间不确定表示下的可恢复鲁棒最短路径问题。已知该问题具有强NP难性，且在有向图中难以近似求解。本文聚焦于无环有向图类的研究。研究表明，在传统区间不确定模型下，针对文献中已知的所有自然邻域结构，该问题可在多项式时间内求解。本文为不同类别的无环有向图构建了高效算法，并强化了一般有向图中的部分否定性结论。最后，针对预算区间不确定情形，提出了若干精确求解与近似求解方法。