The shortest path problem in graphs is fundamental to AI. Nearly all variants of the problem and relevant algorithms that solve them ignore edge-weight computation time and its common relation to weight uncertainty. This implies that taking these factors into consideration can potentially lead to a performance boost in relevant applications. Recently, a generalized framework for weighted directed graphs was suggested, where edge-weight can be computed (estimated) multiple times, at increasing accuracy and run-time expense. We build on this framework to introduce the problem of finding the tightest admissible shortest path (TASP); a path with the tightest suboptimality bound on the optimal cost. This is a generalization of the shortest path problem to bounded uncertainty, where edge-weight uncertainty can be traded for computational cost. We present a complete algorithm for solving TASP, with guarantees on solution quality. Empirical evaluation supports the effectiveness of this approach.

翻译：图论中的最短路径问题是人工智能的基础。几乎所有该问题的变体及其求解算法都忽略了边权重计算时间及其与权重不确定性的常见关联。这意味着将这些因素纳入考虑可在相关应用中带来性能提升。近期，有研究提出了一种适用于加权有向图的通用框架，该框架允许以递增的精度和耗时重复计算（估计）边权重。我们基于该框架提出了"最紧允许最短路径"（TASP）问题：即寻找具有最优代价最紧次优性界限的路径。这是最短路径问题在含界不确定性下的泛化，其中边权重的不确定性可通过计算成本进行权衡。我们提出了一种完整的TASP求解算法，并给出了解质量的保证。实证评估支持了该方法的有效性。