Canadian Traveller Problem with Predictions

TL;DR

This paper studies the $k$-Canadian Traveller Problem under a learning-augmented framework, proposing algorithms that balance solution quality with prediction accuracy, and establishing optimal tradeoffs and bounds.

Contribution

It introduces deterministic and randomized algorithms for $k$-CTP with prediction, and proves matching lower bounds for the tradeoff between consistency and robustness.

Findings

Achieves optimal tradeoff between consistency and robustness.

Provides lower bounds matching the performance of proposed algorithms.

Establishes bounds on competitive ratio depending on prediction error.

Abstract

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.