Tightest Admissible Shortest Path

• URL: http://arxiv.org/abs/2308.08453v2
• Date: Wed, 27 Mar 2024 21:46:41 GMT
• Title: Tightest Admissible Shortest Path
• Authors: Eyal Weiss, Ariel Felner, Gal A. Kaminka,
• Abstract summary: shortest path problem in graphs is fundamental to AI. We introduce the problem of finding the admissible shortest path (TASP), a path with the tightest suboptimality bound on the optimal cost. We present a complete algorithm for solving TASP, with guarantees on solution quality.
• Score: 4.928034044959278
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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