optrees (version 1.0)

findMinCut: Finds the minimum cut of a given graph

Description

The findMinCut function can find the minimum cut of a given graph. For that, this function computes the maximum flow of the network and applies the max-flow min-cut theorem to determine the cut with minimum weight between the source and the sink nodes.

Usage

findMinCut(nodes, arcs, algorithm = "Ford-Fulkerson", source.node = 1, sink.node = nodes[length(nodes)], directed = FALSE)

Arguments

nodes

vector containing the nodes of the graph, identified by a number that goes from $1$ to the order of the graph.

arcs

matrix with the list of arcs of the graph. Each row represents one arc. The first two columns contain the two endpoints of each arc and the third column contains their weights.

algorithm

denotes the algorithm used to compute the maximum flow: "Ford-Fulkerson".

source.node

number pointing to the source node of the graph. It's node $1$ by default.

sink.node

number pointing to the sink node of the graph. It's the last node by default.

directed

logical value indicating whether the graph is directed (TRUE) or not (FALSE).

Value

findMinCut returns a list with:

s.cut

vector with the nodes of the s cut.

t.cut

vector with the nodes of the t cut.

max.flow

value with the maximum flow in the flow network.

cut.set

list of arcs of the cut set founded.

Details

The max-flow min-cut theorem proves that, in a flow network, the maximum flow between the source node and the sink node and the weight of any minimum cut between them is equal.

See Also

This function is an auxiliar function used in ghTreeGusfield and getMinimumCutTree.

Examples

# Graph
nodes <- 1:6
arcs <- matrix(c(1,2,1, 1,3,7, 2,3,1, 2,4,3, 2,5,2, 3,5,4, 4,5,1, 4,6,6,
                5,6,2), byrow = TRUE, ncol = 3)
# Find minimum cut
findMinCut(nodes, arcs, source.node = 2, sink.node = 6)