  Correlation clustering is arguably the most natural formulation of
clustering. Given n objects and a pairwise similarity measure, the goal is to
cluster the objects so that, to the best possible extent, similar objects are
put in the same cluster and dissimilar objects are put in different clusters.
  A main drawback of correlation clustering is that it requires as input the
$\Theta(n^2)$ pairwise similarities. This is often infeasible to compute or
even just to store. In this paper we study \emph{query-efficient} algorithms
for correlation clustering. Specifically, we devise a correlation clustering
algorithm that, given a budget of $Q$ queries, attains a solution whose
expected number of disagreements is at most $3\cdot OPT + O(\frac{n^3}{Q})$,
where $OPT$ is the optimal cost for the instance. Its running time is $O(Q)$,
and can be easily made non-adaptive (meaning it can specify all its queries at
the outset and make them in parallel) with the same guarantees. Up to constant
factors, our algorithm yields a provably optimal trade-off between the number
of queries $Q$ and the worst-case error attained, even for adaptive algorithms.
  Finally, we perform an experimental study of our proposed method on both
synthetic and real data, showing the scalability and the accuracy of our
algorithm.
