Before revision:  Our decremental hopset algorithm allows us to obtain the following improved decremental algorithms for maintaining shortest paths. -} (1+\epsilon)-approximate single-source shortest paths with amortized update time of 2^{\tilde{O}(\sqrt{\log n})} , when 0< \epsilon<1 is a constant and |E|= n2^{\tilde{\Omega(\sqrt{\log n})}} . This improves  over the best known  update time of 2^{\tilde{O}(\log^{3/4} n)} by [ Henzinger, Krinninger and Nanongkai, FOCS'14].
After revision:  Our decremental hopset algorithm allows us to obtain the following improved decremental algorithms for maintaining shortest paths. -} (1+\epsilon)-approximate single-source shortest paths with amortized update time of 2^{\tilde{O}(\sqrt{\log n})} (\sqrt{\log n})}} . This improves over the best known update time of 2^{\tilde{O}(\log^{3/4} n)} by [ Henzinger, Krinninger and Nanongkai, FOCS'14].