Is Max flow problem NP-complete?

The maximum flow problem with minimum quantities was introduced in [4], where the problem was shown to be weakly NP-complete even on series-parallel graphs and Lagrangean relaxation techniques and heuristics for solving the problem were studied.

Is Ford Fulkerson NP hard?

1 Answer. Yes, the Ford-Fulkerson algorithm is a pseudopolynomial time algorithm. Its runtime is O(Cm), where C is the sum of the capacities leaving the start node. Since writing out the number C requires O(log C) bits, this runtime is indeed pseudopolynomial but not actually polynomial.

What is maximal flow problem explain with an example?

Maximum flow problems involve finding a feasible flow through a single-source, single-sink flow network that is maximum. Let’s take an image to explain how the above definition wants to say. Each edge is labeled with capacity, the maximum amount of stuff that it can carry.

How is the augmenting path algorithm used in max flow problem?

This is an iterative method (operates in stages) •At each iteration, the algorithm is searching for a path from the source node to the sink node along which it can send a positive flow •Such a path is referred to as augmenting path •After a flow is sent along an augmenting path the capacities of the links on that path are adjusted

When was the maximum flow problem first formulated?

The maximum flow problem was first formulated in 1954 by T. E. Harris and F. S. Ross as a simplified model of Soviet railway traffic flow.

Which is the best solution to the maximum flow problem?

Over the years, various improved solutions to the maximum flow problem were discovered, notably the shortest augmenting path algorithm of Edmonds and Karp and independently Dinitz; the blocking flow algorithm of Dinitz; the push-relabel algorithm of Goldberg and Tarjan; and the binary blocking flow algorithm of Goldberg and Rao.

Is the maximum flow problem guaranteed to terminate?

The following table lists algorithms for solving the maximum flow problem. The algorithm is only guaranteed to terminate if all weights are rational. Otherwise it is possible that the algorithm will not converge to the maximum value. However, if the algorithm terminates, it is guaranteed to find the maximum value.