# Does Ford-Fulkerson work for undirected graph?

## Does Ford-Fulkerson work for undirected graph?

Abstract This work presents an algorithm for computing the maximum flow and minimum cut of undirected graphs, based on the well-known algorithm presented by Ford and Fulkerson for directed graphs.

## What is maximum flow graph?

A maximum flow is defined as the maximum amount of flow that the graph or network would allow to flow from the source node to its sink node.

Is max flow in NP?

As for whether this problem is in P or NP-complete, because we have algorithms for max-flow whose runtime is strongly polynomial (not pseudopolynomial), the max-flow problem is definitely in P.

### How do you tell if a flow is a max-flow?

A flow is maximum if there is no s-t path in the residual network. You can check this in time O(|E|).

Is Ford-Fulkerson NP complete?

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 the maximum flow method?

It is defined as the maximum amount of flow that the network would allow to flow from source to sink. Multiple algorithms exist in solving the maximum flow problem. Two major algorithms to solve these kind of problems are Ford-Fulkerson algorithm and Dinic’s Algorithm.

## What is the maximum flow value?

The maximum value of an s-t flow (i.e., flow from source s to sink t) is equal to the minimum capacity of an s-t cut (i.e., cut severing s from t) in the network, as stated in the max-flow min-cut theorem.

Is max-flow in NP?

### What is max flow in a graph?

A residual network graph indicates how much more flow is allowed in each edge in the network graph. If there are no augmenting paths possible from to , then the flow is maximum. The result i.e. the maximum flow will be the total flow out of source node which is also equal to total flow in to the sink node.