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领域的基础问题。几乎所有问题变体及其求解算法都忽略了边权计算时间及其与权值不确定性之间的常见关联。这意味着将这两个因素纳入考量，有望在相关应用中实现性能提升。近期，有学者针对带权有向图提出了一个通用框架，允许通过多次计算（估算）边权来逐步提升精度，但会相应增加运行时间开销。我们基于该框架提出"最紧可容许最短路径"（TASP）问题：即寻找具有最紧次优性界的最优代价路径。这是将最短路径问题推广至有界不确定性场景，其中边权不确定性可通过计算成本进行权衡。我们提出一种完整的TASP求解算法，并给出解的质量保证。实证评估验证了该方法的有效性。