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

A Generalization of the Shortest Path Problem to Graphs with Multiple Edge-Cost Estimates