Initially, the flow of value is 0. Find some augmenting Path p and increase flow f on each edge of p by residual Capacity c f (p). When no augmenting path exists, flow f is a maximum flow. FORD-FULKERSON METHOD (G, s, t) 1. Initialize flow f to 0 2. while there exists an augmenting path p 3. do argument flow f along p 4. Ford-Fulkerson algorithm: pathological example Theorem. The Ford-Fulkerson algorithm may not terminate; moreover, it may converge to a value not equal to the value of the maximum flow. Pf. ・After (1 + 4k) augmenting paths of the form just described, the value of the flow ・Value of maximum flow = 2C + 1. 33 =1+2 2k Ford Fulkerson algorithm - Free download as Powerpoint Presentation (.ppt / .pptx), PDF File (.pdf), Text File (.txt) or view presentation slides online. Ford Fulkerson algorithm solving the problem, Lester Randolph Ford Jr. and Delbert Ray Fulkerson created the first known algorithm for the maximum flow problem in 1955; the name of the algorithm taking their very surnames: Ford-Fulkerson algorithm. Figure 2. Railway system of western Russia fetched from Ford-Fulkerson's secret documentation The Ford-Fulkerson Labeling Algorithm: Convention First, a convention: The algorithm begins with a linear order on the vertex set which establishes a notion of precedence. Typically, the rst vertex in this linear order is the source while the second is the sink. After that, the vertices can be listed in any order.