I'm looking for a fast algorithm to compute maximum flow in dynamic graphs. i.e given a graph $G=(V,E)$ and $s,t\in V$ we have maximum flow $F$ in $G$ from $s$ to the $t$. Then new/old node $u$ added/deleted with its corresponding edges to form a graph $G^1$. What is a maximum flow in newly created graph? Is there a way to prevent from recalculating maximum flow?
Any preprocessing which isn't very time/memory consuming is appreciated.
Simplest idea is recalculating the flow.
Another simple idea is as this, save all augmenting paths which used in previous maximum flow calculation, for adding a vertex $v$, we can find simple paths (in updated capacity graph by previous step) which start from source, goes to the $v$ then goes to the destination, but problem is, this path should be simple, I couldn't find better than $O(n\cdot m)$ for this case, for $m=|E|$. (Also note that if it was just one path this could be done in $O(n+m)$ but it's not so.)
Also for removing node above idea doesn't work.
Also I already saw papers such as Incremental approach for edges, but seems they are not good enough in this case, it's more than $O(m)$ for each edge and seems is not suitable extension in this case (we just recalculate a flow). Also currently I'm using Ford-Fulkerson maximum flow algorithm If there is better option for online algorithms, it's good to know it.