Before revision:  The currently best known algorithm for the problem is obtained by running the single-source algorithm of Henzinger, Krinninger and Nanongkai, FOCS'14 independently from each source. Our result improves over the update time bound of this solution by removing a 2 ^{\tilde{O(\log^{3/4} n)} factor.
After revision:  The currently best known algorithm for the problem is obtained by running the single-source algorithm of Henzinger, Krinninger and Nanongkai, FOCS'14 . Previously, the best known decremental hopset algorithm had a hopbound of 2 ^{\tilde{O(\log^{3/4} n)} factor.