Before revision:  In this paper , we obtain the first dynamic algorithm for this problem with near-optimal approximation ratio whose update timeis independent of m, n(\epsilon)) worst-case update time for unweighted dynamic vertex cover (i.e., when f=2 and C=1) by Bhattacharya et al.
After revision:  In this paper we improve the latter update time and provide the first bounds that subsume (and sometimes improve) the state-of-the-art dynamic vertex cover algorithms. We obtain: 1. (1+\epsilon)f-approximation ratio in O(f\log^2 (Cn)/\epsilon^3) worst-case update time: No non-trivial worst-case update time was previously known for dynamic set cover. Our bound subsumes and improves by a logarithmic factor the O(\log^3 n/\text{poly(\epsilon)) worst-case update time for unweighted dynamic vertex cover (i.e., when f=2 and C=1) by Bhattacharya et al.