ENGRI 1101
Engineering Applications of OR
Fall ’09
Homework 2
The Shortest Path Problem
Due date: 4pm on September 16, 2009 in Rhodes ENGRI 1101 dropbox.
Reading assignment: Handout 3 on the shortest path problem.
Be sure to write which lab you attend and your NETID at the top of your homework.
1. (70) Suppose that you are given the graph
G
= (
N, A
) with
N
=
{
1
,
2
,
3
,
4
,
5
}
and
A
=
{
(1
,
2)
,
(1
,
3)
,
(2
,
1)
,
(2
,
3)
,
(2
,
5)
,
(3
,
1)
,
(3
,
4)
,
(4
,
2)
,
(5
,
3)
,
(5
,
4)
}
and a special source node
s
= 6 . The lengths of these arcs are given in the table below:
(
i, j
)
‘
(
i, j
)
(1,2)
2
(1,3)
6
(2,1)
3
(2,3)
4
(2,5)
3
(3,1)
2
(3,4)
1
(4,2)
6
(5,3)
1
(5,4)
5
Be sure to explain ALL of your work.
(a) (5) Draw a picture of the directed graph
G
.
(b) (5) Is (1
,
2) , (2
,
3) , (3
,
5) a path from node 1 to node 5 in this graph? Why or why not?
(c) (5) Is (4
,
3)
∈
N
? is (4
,
3)
∈
A
?
(d) (20) Compute the length of the shortest path from the source node 5 to each other node.
(e) (5) Compute the shortest path (the path, not its length) from node 5 to node 2.
(f) (10) Compute the shortest path tree for this input.