Generalized Sorting with Predictions

TL;DR

This paper introduces algorithms for generalized sorting that leverage predictions to reduce the number of probes needed, achieving near-optimal efficiency depending on prediction accuracy.

Contribution

It presents both randomized and deterministic algorithms for generalized sorting with predictions, improving probe complexity based on prediction mistakes.

Findings

Randomized algorithm uses O(n log n + w) probes with high probability.

Deterministic algorithm uses O(nw) probes, where w is the number of prediction mistakes.

The approach adapts to prediction accuracy, enhancing efficiency over traditional methods.

Abstract

Generalized sorting problem, also known as sorting with forbidden comparisons, was first introduced by Huang et al. together with a randomized algorithm which requires $\tilde O(n^{3/2})$ probes. We study this problem with additional predictions for all pairs of allowed comparisons as input. We propose a randomized algorithm which uses $O(n \log n+w)$ probes with high probability and a deterministic algorithm which uses $O(nw)$ probes, where $w$ is the number of mistakes made by prediction.