Approximation algorithm:

Keep grabbing edges whose vertices are not already in the cover

Approx-Vertex-Cover(G)
; G = (V, E)

C = {}

E' = E

while E' {}

(u,v) = arbitrary edge from E'

C = C {u,v}

remove from E' every edge incident on u or v

return C

This algorithm takes O(E) time.