  We study approximability of subdense instances of various covering problems
on graphs, defined as instances in which the minimum or average degree is
Omega(n/psi(n)) for some function psi(n)=omega(1) of the instance size. We
design new approximation algorithms as well as new polynomial time
approximation schemes (PTASs) for those problems and establish first
approximation hardness results for them. Interestingly, in some cases we were
able to prove optimality of the underlying approximation ratios, under usual
complexity-theoretic assumptions. Our results for the Vertex Cover problem
depend on an improved recursive sampling method which could be of independent
interest.
