With a reasonably accurate predictor for nodes in the solution, simple linear-time algorithms achieve (1-ε) approximation for densest subgraph and its densest at-most-k variant.
Are stable instances easy?Combinatorics, Probability and Computing, 21(5):643–660, 2012
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Fast and Simple Densest Subgraph with Predictions
With a reasonably accurate predictor for nodes in the solution, simple linear-time algorithms achieve (1-ε) approximation for densest subgraph and its densest at-most-k variant.