Tightest Admissible Shortest Path

TL;DR

This paper introduces the TASP problem, optimizing shortest paths under edge-weight uncertainty and computational cost, with a complete algorithm and empirical validation demonstrating improved performance.

Contribution

It formulates the TASP problem, generalizing shortest path to uncertain weights, and provides a complete algorithm with guarantees on solution quality.

Findings

The algorithm effectively finds tightest admissible paths.

Empirical results show performance improvements.

The framework balances accuracy and computation time.

Abstract

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.