EdmondsKarpalgoritmen

The Edmonds-Karp algorithm is a specific implementation of the Ford-Fulkerson method for computing the maximum flow in a flow network. It was developed by Jack Edmonds and Richard Karp. The core idea of the Ford-Fulkerson method is to repeatedly find augmenting paths from the source to the sink in the residual graph and increase the flow along these paths until no more augmenting paths can be found.

What distinguishes the Edmonds-Karp algorithm is its strategy for selecting augmenting paths. It specifically chooses the shortest augmenting path in terms of the number of edges. This is achieved by using a Breadth-First Search (BFS) algorithm to find the shortest path in the residual graph. The BFS explores the graph level by level, guaranteeing that the first path found from the source to the sink will be the one with the fewest edges.

The use of BFS ensures that the algorithm terminates and provides a polynomial time complexity. The time complexity of the Edmonds-Karp algorithm is O(VE^2), where V is the number of vertices and E is the number of edges in the graph. This is a significant improvement over the general Ford-Fulkerson method, which can have exponential time complexity in certain pathological cases. The algorithm works by maintaining a residual graph, which represents the remaining capacity of edges. When flow is pushed along a path, the residual capacities are updated, and backward edges are introduced to allow for flow cancellation. The process continues until BFS can no longer find a path from the source to the sink in the residual graph.