  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.
