Approximability of the vertex cover problem in power-law graphs

In this paper we construct an approximation algorithm for the Minimum Vertex Cover (Min-VC) problem with an expected approximation ratio of [email protected](@b)-1-12^@b2^@[email protected](@b-1)@z(@b) for random power-law graphs in the P(@a,@b) model due to Aiello et al. Here @z(@b) is the Riemann zeta function of @b. We obtain this result by combining the Nemhauser and Trotter approach for Min-VC with a new deterministic rounding procedure which achieves an approximation ratio of 32 on a subset of low degree vertices for which the expected contribution to the cost of the associated linear program is sufficiently large.

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