Is it possible a Floyd's Algorithm of O(|v|^2)???

Is it possible to have a version of Floyd's Algorithm of just O(|v|^2)?
If yes, what would it be?

Thanks.

- The Floyd's Algorithm is a common algorithm to find shortest paths in weighted graphs of O(|v|^3) -.

Just thinking aloud here...

Perhaps it is possible for incremental computation and would be useful for certain kinds of applications where time amortization is useful. That is you compute the matrix for n vertices and for a new vertex n+1, you compute only a small subset. I believe there is an efficient algorithm for incremental matrix re-computation which can be used when only one element changes. (I vaguely remember seeing something for determinant computation...)