aiqbench analysis
This research bridges classical optimization theory and machine learning by providing provable guarantees for converting neural network heatmaps into valid Traveling Salesperson Problem tours. The proposed algorithms explicitly link approximation ratios to prediction quality, addressing a critical gap in existing ML-based approaches that lacked theoretical bounds on solution performance. This work advances the field of algorithmic machine learning where AI models serve as predictors within rigorous computational frameworks rather than standalone black boxes.
TSP with Predictions: Heatmap to Tour with Provable Guarantees
arXiv:2607.03791v2 Announce Type: replace-cross Abstract: The Traveling Salesperson Problem (TSP) has long served as a benchmark for evaluating the strength of optimization techniques in the classical theory of algorithms. In recent efforts to apply ML to algorithmic problems, TSP has also become a natural testbed for the development of ML-based techniques. A common approach is to train a neural network to output a heatmap estimating the likelihood of each edge to be part of the optimal tour; however, converting such a heatmap into an actual tour remains a non-trivial and often computationally intensive step. In this work, we propose algorithms for transforming heatmaps into tours with theoretical guarantees linking the achieved approximation ratio to the quality of the provided heatmap. In the spirit of algorithms with predictions, our results can be described as $(1+2\frac{\eta}{\mathrm{OPT}})$-approximation algorithms, where $\eta$ denotes the L1 distance between the prediction (heatmap) and an optimal solution (tour). Since the previous works lack such explicit guarantees, we compare our approach against them experimentally.
Abstract:The Traveling Salesperson Problem (TSP) has long served as a benchmark for evaluating the strength of optimization techniques in the classical theory of algorithms. In recent efforts to apply ML to algorithmic problems, TSP has also become a natural testbed for the development of ML-based techniques. A common approach is to train a neural network to output a heatmap estimating the likelihood of each edge to be part of the optimal tour; however, converting such a heatmap into an actual tour remains a non-trivial and often computationally intensive step. In this work, we propose algorithms for transforming heatmaps into tours with theoretical guarantees linking the achieved approximation ratio to the quality of the provided heatmap. In the spirit of algorithms with predictions, our results can be described as $(1+2\frac{\eta}{\mathrm{OPT}})$-approximation algorithms, where $\eta$ denotes the L1 distance between the prediction (heatmap) and an optimal solution (tour). Since the previous works lack such explicit guarantees, we compare our approach against them experimentally.
Data Structures and Algorithms (cs.DS); Machine Learning (cs.LG)
arXiv:2607.03791 [cs.DS]
(or arXiv:2607.03791v2 [cs.DS] for this version)
https://doi.org/10.48550/arXiv.2607.03791 Focus to learn more arXiv-issued DOI via DataCite
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