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

TL;DR

The paper generalizes shortest-path search to graphs where edge costs are obtained via multiple estimators that provide lower and upper bounds at increasing cost. It formalizes the Shortest-Path Tightest Lower Bound (SLB) problem on an estimated weighted digraph G=(V,E,Θ) and presents two complete algorithms, BEAUTY and Anytime BEAUTY, which couple best-first search with dynamic weight estimation to guarantee optimal SLB solutions. Empirical results on AI planning benchmarks show substantial reductions (approximately 40–55%) in expensive edge evaluations compared with a baseline that uses the most accurate estimates, at manageable increases in search effort. The work demonstrates practical benefits for planning and search in scenarios with expensive or external weight computations and lays groundwork for future extensions to other SLB variants and graph settings.

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.

Figures (1)

• Figure 1: Left: Digraph of Example \ref{['example:graph']}. Right: costs and estimates.

Theorems & Definitions (16)

• Definition 1
• Definition 2
• Definition 3
• Theorem 1
• proof
• Example 1
• Lemma 1: Conditional Completeness Prob. \ref{['prob:l']}
• proof
• Lemma 2: Bounds for $L^*$
• proof