Edmonds–Karp algorithm
In computer science, the Edmonds–Karp algorithm is an implementation of the Ford–Fulkerson method for computing the maximum flow in a flow network inThe algorithm was first published by Yefim Dinitz in 1970,[1][2] and independently published by Jack Edmonds and Richard Karp in 1972.[3] Dinitz's algorithm includes additional techniques that reduce the running time to[2] The algorithm is identical to the Ford–Fulkerson algorithm, except that the search order when finding the augmenting path is defined.This can be found by a breadth-first search, where we apply a weight of 1 to each edge.edges becomes saturated (an edge which has the maximum possible flow), that the distance from the saturated edge to the source along the augmenting path must be longer than last time it was saturated, and that the length is at mostAnother property of this algorithm is that the length of the shortest augmenting path increases monotonically.There is an accessible proof in Introduction to Algorithms.[4] Given a network of seven nodes, source A, sink G, and capacities as shown below:, the total capacity, minus the flow that is already used.is negative, it contributes to the residual capacity.Notice how the length of the augmenting path found by the algorithm (in red) never decreases.The flow found is equal to the capacity across the minimum cut in the graph separating the source and the sink.There is only one minimal cut in this graph, partitioning the nodes into the sets
computer scienceFord–Fulkerson methodmaximum flowflow network
O
(
|
V
|
|
E
|
2
)
{\displaystyle O(|V||E|^{2})}
Yefim DinitzJack EdmondsRichard KarpDinitz's algorithmFord–Fulkerson algorithmbreadth-first searchIntroduction to Algorithmsaugmenting pathminimum cutDinic, E. A.Oded GoldreichAlan L. SelmanShimon EvenEdmonds, JackKarp, Richard M.Thomas H. CormenCharles E. LeisersonRonald L. RivestClifford SteinOptimizationAlgorithmsmethodsheuristicsUnconstrained nonlinearFunctionsGolden-section searchPowell's methodLine searchNelder–Mead methodSuccessive parabolic interpolationGradientsConvergenceTrust regionWolfe conditionsQuasi–NewtonBerndt–Hall–Hall–HausmanBroyden–Fletcher–Goldfarb–ShannoL-BFGSDavidon–Fletcher–PowellSymmetric rank-one (SR1)Other methodsConjugate gradientGauss–NewtonGradientMirrorLevenberg–MarquardtPowell's dog leg methodTruncated NewtonHessiansNewton's methodConstrained nonlinearBarrier methodsPenalty methodsAugmented Lagrangian methodsSequential quadratic programmingSuccessive linear programmingConvex optimizationConvex minimizationCutting-plane methodReduced gradient (Frank–Wolfe)Subgradient methodLinearquadraticAffine scalingEllipsoid algorithm of KhachiyanProjective algorithm of KarmarkarBasis-exchangeSimplex algorithm of DantzigRevised simplex algorithmCriss-cross algorithmPrincipal pivoting algorithm of LemkeActive-set methodCombinatorialApproximation algorithmDynamic programmingGreedy algorithmInteger programmingBranch and boundGraph algorithmsMinimum spanning treeBorůvkaKruskalShortest pathBellman–FordDijkstraFloyd–WarshallNetwork flowsFord–FulkersonPush–relabel maximum flowMetaheuristicsEvolutionary algorithmHill climbingLocal searchParallel metaheuristicsSimulated annealingSpiral optimization algorithmTabu searchSoftware