# Tight query complexity bounds for learning graph partitions

@inproceedings{Liu2022TightQC, title={Tight query complexity bounds for learning graph partitions}, author={Xizhi Liu and Sayan Mukherjee}, booktitle={COLT}, year={2022} }

Given a partition of a graph into connected components, the membership oracle asserts whether any two vertices of the graph lie in the same component or not. We prove that for n ≥ k ≥ 2, learning the components of an n -vertex hidden graph with k components requires at least ( k − 1) n − (cid:0) k 2 (cid:1) membership queries. Our result improves on the best known information-theoretic bound of Ω( n log k ) queries, and exactly matches the query complexity of the algorithm introduced by Reyzin…

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