No online algorithm finds common induced subgraphs of size (2+ε)log₂n with probability bounded away from zero in Erdős–Rényi graphs G(n,1/2), while the optimum is (4-o(1))log₂n and greedy achieves (2-o(1))log₂n.
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Optimal Hardness of Online Algorithms for Large Common Induced Subgraphs
No online algorithm finds common induced subgraphs of size (2+ε)log₂n with probability bounded away from zero in Erdős–Rényi graphs G(n,1/2), while the optimum is (4-o(1))log₂n and greedy achieves (2-o(1))log₂n.