Before revision:  - ( 1+\epsilon)-approximate shortest paths from a set of s sources in (s) amortized update time, assuming that s= n^{\Omega(1), and |E|= n^{1+\Omega(1)}.
After revision:  - ( 1+\epsilon)-approximate shortest paths from a set of s sources in , and |E|= n^{1+\Omega(1)}.