findMinCut: Finds the minimum cut of a given graph

In optrees: Optimal Trees in Weighted Graphs

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).

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.

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.

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)

Example output

Loading required package: igraph

Attaching package: 'igraph'

The following objects are masked from 'package:stats':

    decompose, spectrum

The following object is masked from 'package:base':

    union

$s.cut
[1] 2 3 1 5

$t.cut
[1] 4 6

$max.flow
[1] 6

$cut.set
     ept1 ept2 weight
[1,]    2    4      3
[2,]    5    4      1
[3,]    5    6      2

optrees documentation built on May 2, 2019, 8:15 a.m.