Tightest Admissible Shortest Path
This addresses a problem in AI for applications where edge-weight computation time and uncertainty are critical, representing an incremental advance building on a recent generalized framework.
The paper tackles the shortest path problem by introducing the tightest admissible shortest path (TASP), which generalizes it to bounded uncertainty where edge-weight uncertainty can be traded for computational cost, and presents a complete algorithm with guarantees on solution quality, supported by empirical evaluation.
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.