Counting connected components in induced subgraphs reconstructs any n-node m-edge graph with Θ(m log n / log m) adaptive queries, while non-adaptive algorithms need Ω(n²).
Cut query algorithms with star contraction
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Optimal Graph Reconstruction by Counting Connected Components in Induced Subgraphs
Counting connected components in induced subgraphs reconstructs any n-node m-edge graph with Θ(m log n / log m) adaptive queries, while non-adaptive algorithms need Ω(n²).