Polynomial Time Learning-Augmented Algorithms for NP-hard Permutation Problems

TL;DR

This paper introduces a learning-augmented approach for NP-hard permutation problems, leveraging predictions to solve problems like scheduling and network design in polynomial time when predictions are sufficiently accurate.

Contribution

It demonstrates that predictions can be used to solve certain NP-hard permutation problems efficiently with high probability, extending prior work to a broader class of problems.

Findings

Predictions enable polynomial-time solutions for NP-hard permutation problems.

High-probability success when prediction accuracy exceeds 50%.

Efficient use of predictions with minimal access.

Abstract

We consider a learning-augmented framework for NP-hard permutation problems. The algorithm has access to predictions telling, given a pair $u,v$ of elements, whether $u$ is before $v$ or not in an optimal solution. Building on the work of Braverman and Mossel (SODA 2008), we show that for a class of optimization problems including scheduling, network design and other graph permutation problems, these predictions allow to solve them in polynomial time with high probability, provided that predictions are true with probability at least $1/2+\epsilon$. Moreover, this can be achieved with a parsimonious access to the predictions.