Exact optimal correlation clustering is recoverable with at most 2*COPT same-cluster queries, and a 2-approximation with at most COPT queries; a Gap-ETH lower bound rules out o(COPT)-query (1+alpha)-approximations.
Going weighted: Parameterized algorithms for cluster editing
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Correlation Clustering with Same-Cluster Queries Bounded by Optimal Cost
Exact optimal correlation clustering is recoverable with at most 2*COPT same-cluster queries, and a 2-approximation with at most COPT queries; a Gap-ETH lower bound rules out o(COPT)-query (1+alpha)-approximations.