Canadian Traveller Problem with Predictions
Résumé
In this work, we consider the k-Canadian Traveller Problem (k-CTP) under the learning-augmented framework proposed by Lykouris & Vassilvitskii. k-CTP is a generalization of the shortest path problem, and involves a traveller who knows the entire graph in advance and wishes to find the shortest route from a source vertex s to a destination vertex t, but discovers online that some edges (up to k) are blocked once reaching them. A potentially imperfect predictor gives us the number and the locations of the blocked edges.
We present a deterministic and a randomized online algorithm for the learning-augmented k-CTP that achieve a tradeoff between consistency (quality of the solution when the prediction is correct) and robustness (quality of the solution when there are errors in the prediction). Moreover, we prove a matching lower bound for the deterministic case establishing that the tradeoff between consistency and robustness is optimal, and show a lower bound for the randomized algorithm. Finally, we prove several deterministic and randomized lower bounds on the competitive ratio of k-CTP depending on the prediction error, and complement them, in most cases, with matching upper bounds.