17.12.2012

We give logarithmic lower bounds for the approximability of the Minimum Dominating Set problem in connected (α,β)-Power Law Graphs. We give also a best up to now upper approximation bound on the problem for the case of the parameters β > 2. We develop also a new functional method for proving lower approximation bounds and display a sharp phase transition between approximability and inapproximability of the underlying problem. This method could also be of independent interest.