Before revision: }}%DIFAUXCMD \addtocounter{footnote}{-1}%DIFAUXCMD . This improves over the result of\tilde{O})\cdot(1/\epsilon)^{O(\sqrt{\log n})} } [Chechik, FOCS'18] in a twofold way. Namely, we improve the total update time bound by removing an n^{o(1) reduce the query time from O(\log \log (nW)) to  O(k) . Our results are based on a new decremental hopset construction that may be of independent interest .
After revision: }}%DIFAUXCMD \addtocounter{footnote}{-1}%DIFAUXCMD . This improves over the result of\tilde{O})\cdot(1/\epsilon)^{O(\sqrt{\log n})} } [Chechik, FOCS'18] . Moreover, we reduce the query time from O(\log \log (nW)) to O(k) . Our results are based on a new decremental hopset construction that may be of independent interest .