Search results
Results From The WOW.Com Content Network
The Ford–Fulkerson method or Ford–Fulkerson algorithm (FFA) is a greedy algorithm that computes the maximum flow in a flow network.It is sometimes called a "method" instead of an "algorithm" as the approach to finding augmenting paths in a residual graph is not fully specified [1] or it is specified in several implementations with different running times. [2]
Ford–Fulkerson algorithm: 1955 As long as there is an open path through the residual graph, send the minimum of the residual capacities on that path. Edmonds–Karp algorithm: 1970 A specialization of Ford–Fulkerson, finding augmenting paths with breadth-first search. Dinic's algorithm: 1970
This concept is used in Ford–Fulkerson algorithm which computes the maximum flow in a flow network. Note that there can be an unsaturated path (a path with available capacity) from u to v in the residual network, even though there is no such path from u to v in the original network.
The Ford–Fulkerson algorithm, a greedy algorithm for maximum flow that is not in general strongly polynomial; The network simplex algorithm, a method based on linear programming but specialized for network flow [1]: 402–460 The out-of-kilter algorithm for minimum-cost flow [1]: 326–331
After graduation, Fulkerson joined the mathematics department at the RAND Corporation. In 1956, he and L. R. Ford Jr. described the Ford–Fulkerson algorithm. [3] In 1962 they produced a book-length description of their method. [4] In 1971 he moved to Cornell University as the Maxwell Upson Professor of Engineering.
Consider the flow f computed for G by Ford–Fulkerson algorithm. In the residual graph (G f ) obtained for G (after the final flow assignment by Ford–Fulkerson algorithm), define two subsets of vertices as follows: A: the set of vertices reachable from s in G f; A c: the set of remaining vertices i.e. V − A
The algorithm is identical to the Ford–Fulkerson algorithm, except that the search order when finding the augmenting path is defined. The path found must be a shortest path that has available capacity. This can be found by a breadth-first search, where we apply a weight of 1 to each edge.
In comparison, the Ford–Fulkerson algorithm performs global augmentations that send flow following paths from the source all the way to the sink. [1] The push–relabel algorithm is considered one of the most efficient maximum flow algorithms.