The shortest path problem in graphs is a cornerstone of AI theory and applications. Existing algorithms generally ignore edge weight computation time. We present a generalized framework for weighted directed graphs, where edge weight can be computed (estimated) multiple times, at increasing accuracy and run-time expense. This raises several generalized variants of the shortest path problem. We introduce the problem of finding a path with the tightest lower-bound on the optimal cost. We then present two complete algorithms for the generalized problem, and empirically demonstrate their efficacy.

翻译：图中的最短路径问题乃是AI理论与应用的基石。现有算法通常忽略边权重计算时间。我们提出一个针对加权有向图的泛化框架，其中边权重可被多次计算（估计），且计算精度与运行时间成本递增。这衍生出最短路径问题的多个泛化变体。我们引入在最优成本上寻求最紧下界路径的问题，并随后提出两个针对该泛化问题的完备算法，通过实验验证其有效性。