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We study approximability of subdense instances of various covering problemson graphs, defined as instances in which the minimum or average degree isOmega(n/psi(n)) for some function psi(n)=omega(1) of the instance size. Wedesign new approximation algorithms as well as new polynomial timeapproximation schemes (PTASs) for those problems and establish firstapproximation hardness results for them. Interestingly, in some cases we wereable to prove optimality of the underlying approximation ratios, under usualcomplexity-theoretic assumptions. Our results for the Vertex Cover problemdepend on an improved recursive sampling method which could be of independentinterest.

Approximating Subdense Instances of Covering Problems