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