Generalized Sorting with Predictions
Pinyan Lu, Xuandi Ren, Enze Sun, Yubo Zhang

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 probes. We study this problem with additional predictions for all pairs of allowed comparisons as input. We propose a randomized algorithm which uses probes with high probability and a deterministic algorithm which uses probes, where is the number of mistakes made by prediction.
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Taxonomy
TopicsAlgorithms and Data Compression · Genome Rearrangement Algorithms · semigroups and automata theory
