ENGRI 1101 Engineering Applications of OR
Fall 2008 Homework 4
Homework 4 Solutions
1.
(a) First of all one must realize which node is the source and which is the sink. A source is a node
which has net outward flow and a sink is a node which has net inward flow (or equivalently,
negative net outward flow). Summing the flows out of each node in the graph yields 11 for node
1, 0 for nodes 2 through 5, and 11 for node 6. Therefore node 1 must be the souce and node 6
must be the sink. In order to finish the execution of the algorithm we must construct the residual
graph of the figure above, which is shown in the following figure:
There are several several paths from source to sink. We arbitrarily choose path
{
(1,2),(2,3),(3,6)
}
by as much as possible:
δ
= 1 (arc (3,6) is the bottleneck). The graph after we have done the
first iteration is shown below:
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
We then construct the next residual graph:
Again there are several different paths to choose. We choose the path
{
(1,2),(2,3),(3,4),(4,5),(5,6)
}
,
which has
δ
= 1.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '09
 MATTESON
 Graph Theory, Summation, Equals sign, Glossary of graph theory

Click to edit the document details