Before revision:  In this regime, we give the first decremental algorithm, whose running time matches, up to polylogarithmic factors, the best known static algorithm. -} (2k-1)(1+\epsilon)-approximate all-pairs-shortest-paths , in \tilde{O}( mn^{1/k update time and O(k) query time \footnote{Throughout this paper we use the notation (f(n)) to hide factors of O(\text{polylog (f(n))).
After revision:  In this regime, we give the first decremental algorithm, whose running time matches, up to polylogarithmic factors, the best known static algorithm. -} (2k-1)(1+\epsilon)-approximate all-pairs-shortest-paths , in \tilde{O}( mn^{1/k update time and O(k) query time \footnote{Throughout this paper we use the notation (f(n))).