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 in amortized update time }  of 2^{ (\sqrt{\log n } . This improves super-polynomially over the best known amortized update time of 2^{\tilde{O(\log^{3/4} n)} by } [  HKN, 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 in amortized update time } All the previous decremental hopset constructions had a superpolylogarithmic (but subpolynomial) hopbound of 2^{ (\sqrt{\log n } . This improves super-polynomially over the best known amortized update time of 2^{\tilde{O(\log^{3/4} n)} by } [ HKN, FOCS'14 ].