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

TL;DR

This paper extends the shortest path problem to graphs where edge weights can be estimated multiple times with increasing accuracy, proposing new algorithms and demonstrating their effectiveness.

Contribution

It introduces a generalized framework for shortest path problems with multiple edge-cost estimates and provides two complete algorithms for this new problem.

Findings

Algorithms effectively find paths with tightest lower bounds.

Empirical results show improved efficiency over traditional methods.

Framework accommodates multiple estimates, enhancing flexibility.

Abstract

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.