Let NDTIME(f(n),g(n)) denote the class of problems solvable in O(g(n)) time by a multi-tape Turing machine using an f(n)-bit non-deterministic oracle, and let DTIME(g(n)) = NDTIME(0, g(n)). We show that if all-pairs shortest paths problem (APSP) for directed graphs with N vertices integer edge weights within super-exponential range { −2Nk+o(1),....,2Nk+o(1) }, k≥1 does not admit truly subcubic ...