Before revision:  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:  Namely, we improve the total update time bound by removing an n^{o(1) reduce the query time from O(\log \log (nW)) to a constant O(k) . Our results are based on a new decremental hopset construction that may be of independent interest .