Minimum vertex cover in generalized random graphs with power law degree distribution

In this paper we study the approximability of the minimum vertex cover problem in power law graphs. In particular, we investigate the behavior of a standard 2-approximation algorithm together with a simple pre-processing step when the input is a random sample from a generalized random graph model with power law degree distribution. More precisely, if the probability of a vertex of degree i to be present in the graph is ci−β, where β>2 and c is a normalizing constant, the expected approximation ratio is 1+ζ(β)−1Liβ(e−ρ(β)), where ζ(β) is the Riemann Zeta function of β, Li(β) is the polylogarithmic special function of β and ρ(β)=Liβ−2(1e)ζ(β−1).