Sorting and Hypergraph Orientation under Uncertainty with Predictions
This work addresses query minimization under uncertainty for sorting and hypergraph orientation, offering incremental improvements through learning-augmented algorithms with worst-case guarantees.
The paper tackles the problem of minimizing queries in explorable uncertainty settings for sorting and hypergraph orientation by using untrusted predictions, achieving a competitive ratio of 1+1/γ for correct predictions and γ for wrong ones in hypergraph orientation, and optimal solutions for accurate predictions with 2-competitiveness for wrong ones in sorting.
Learning-augmented algorithms have been attracting increasing interest, but have only recently been considered in the setting of explorable uncertainty where precise values of uncertain input elements can be obtained by a query and the goal is to minimize the number of queries needed to solve a problem. We study learning-augmented algorithms for sorting and hypergraph orientation under uncertainty, assuming access to untrusted predictions for the uncertain values. Our algorithms provide improved performance guarantees for accurate predictions while maintaining worst-case guarantees that are best possible without predictions. For hypergraph orientation, for any $γ\geq 2$, we give an algorithm that achieves a competitive ratio of $1+1/γ$ for correct predictions and $γ$ for arbitrarily wrong predictions. For sorting, we achieve an optimal solution for accurate predictions while still being $2$-competitive for arbitrarily wrong predictions. These tradeoffs are the best possible. We also consider different error metrics and show that the performance of our algorithms degrades smoothly with the prediction error in all the cases where this is possible.