Finding large and small dense subgraphs
<|reference_start|>Finding large and small dense subgraphs: We consider two optimization problems related to finding dense subgraphs. The densest at-least-k-subgraph problem (DalkS) is to find an induced subgraph of highest average degree among all subgraphs with at least k vertices, and the densest at-most-k-subgraph problem (DamkS) is defined similarly. These problems are related to the well-known densest k-subgraph problem (DkS), which is to find the densest subgraph on exactly k vertices. We show that DalkS can be approximated efficiently, while DamkS is nearly as hard to approximate as the densest k-subgraph problem.<|reference_end|>
@article{andersen2007finding,
    title={Finding large and small dense subgraphs},
    author={Reid Andersen},
    journal={arXiv preprint arXiv:cs/0702032},
    year={2007},
    archivePrefix={arXiv},
    eprint={cs/0702032},
    primaryClass={cs.DS}
}