Before revision:  Our first result is an algorithm that maintains (1+\epsilon) -approximate distances from a set of s sources in (sm) total update time , assuming that s= n^{\Omega(1), \epsilon = \Omega(1) and |E|= n^{1+\Omega(1)}.
After revision:  Our first result is an algorithm that maintains (1+\epsilon) -approximate distances from a set of s sources in (sm) total update time , \epsilon = \Omega(1) and |E|= n^{1+\Omega(1)}.