Generalized Sorting with Predictions

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(n3/2) 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.