Before revision:  [ FOCS ` 19] very recently led to a deterministic (1+\epsilon)f-approximation algorithm with O(f \log ( Cm )/\epsilon^2)  update time.
After revision:  [ ICALP'15, IPCO'17, FOCS' 19] very recently led to a deterministic (1+\epsilon)f-approximation algorithm with O(f \log ( Cm )/\epsilon^2) update time.