With pairwise predictions that are correct with probability just above 1/2, a class of NP-hard permutation problems (decomposable or c-local objectives) can be solved exactly in polynomial time using only O(n log n) queries.
Learning-Augmented Maximum Independent Set
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Polynomial Time Learning-Augmented Algorithms for NP-hard Permutation Problems
With pairwise predictions that are correct with probability just above 1/2, a class of NP-hard permutation problems (decomposable or c-local objectives) can be solved exactly in polynomial time using only O(n log n) queries.