RBGL (version 1.48.1)

max.flow: Compute max flow for a directed graph

Description

Compute max flow for a directed graph

Usage

edmonds.karp.max.flow(g, source, sink)
push.relabel.max.flow(g, source, sink)
kolmogorov.max.flow(g, source, sink)

Arguments

g

an instance of the graph class with edgemode “directed”

source

node name (character) or node number (int) for the source of the flow

sink

node name (character) or node number (int) for the sink of the flow

Value

A list of

maxflow

the max flow from source to sink

edges

the nodes of the arcs with non-zero capacities

flows

the flow values of the arcs with non-zero capacities

Details

Given a directed graph G=(V, E) of a single connected component with a vertex source and a vertex sink. Each arc has a positive real valued capacity, currently it's equivalent to the weight of the arc. The flow of the network is the net flow entering the vertex sink. The maximum flow problem is to determine the maximum possible value for the flow to the sink and the corresponding flow values for each arc.

See documentation on these algorithms in Boost Graph Library for more details.

References

Boost Graph Library ( www.boost.org/libs/graph/doc/index.html )

The Boost Graph Library: User Guide and Reference Manual; by Jeremy G. Siek, Lie-Quan Lee, and Andrew Lumsdaine; (Addison-Wesley, Pearson Education Inc., 2002), xxiv+321pp. ISBN 0-201-72914-8

See Also

minCut, edgeConnectivity

Examples

con <- file(system.file("XML/dijkex.gxl",package="RBGL"), open="r")
g <- fromGXL(con)
close(con)

ans1 <- edmonds.karp.max.flow(g, "B", "D")
ans2 <- edmonds.karp.max.flow(g, 3, 2)     # 3 and 2 equivalent to "C" and "B"

ans3 <- push.relabel.max.flow(g, 2, 4)     # 2 and 4 equivalent to "B" and "D"
ans4 <- push.relabel.max.flow(g, "C", "B")

# error in the following  now, 14 june 2014
#ans5 <- kolmogorov.max.flow(g, "B", "D")
#ans6 <- kolmogorov.max.flow(g, 3, 2)