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.
A network flow solution to some nonlinear 0-1 programming problems, with applications to graph theory.Networks, 12(2):141–159, 1982
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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.