Algorithm for solving incremental max flow problem

Question

I am working on a project where I need to be able to compute the maximum flow between two nodes in a graph after one of the edge weights has been incremented or decremented by 1. The graph is directed and edge weights are all integers. I can find the maximum flow the first time, by Ford-Fulkerson's algorithm or some variant, but at each step thereafter it would be great if I could use a different (faster) algorithm to find the max flow. At each step, only one of the edge weights is changed, and it is only changed by a value of +1 or -1. What sort of algorithm could do this incremental update for me? It needs to be faster than recomputing the max flow from scratch. It could also be two separate algorithms (but similar I would hope): one for the incrementing case and one for the decrementing case. Thanks in advance for the help!