Thomas J. Naps, Introduction to Data Structures and Algorithm Analysis (2nd edition; West
Publishing Company, 1992), p. 453. ("A Relevant Issue" sidebar titled "Critical path Analysis, PERT,
and CPM", in Chapter 9, Graphs and Networks)
The network shown below represents roughly the activities involved in building a small house.
The events are labeled 0 through 10, with node 0 representing the starting time for the project and
node 10 representing completion time for the project. The dashed edges, marked dummy, are used to
establish precedence relationships only and do not represent real activities of the project. They have an
associated weight of 0. We associate the following completion times with each activity: prepare lot — 3;
lay foundation — 4; erect external frame — 10; erect root — 3; install plumbing — 9; install electrical
wiring — 7; external walls — 7; cover roof — 2; interior walls, floor, and ceiling —; finish exterior — 5;
and finish exterior — 8. Then an examination of the network will show that there is one path in the
network, 0 1 2 3 5 8 9 10, such that any delay in the completion of an activity in this
path will delay the whole project. The length of this path is 39. Paths such as this are known as critical
paths of the network.
5
8
2
dummy
9
Finish
exterior
Prepare
lot
Lay
foundation
Erect
external
frame
Erect
roof
3
Install
plumbing
Install
electrical
wiring
7
External
walls
7
Cover
roof
Interior
walls, floor
ceilings
5
Finish
interior
0
1
2
3
5
4
8
7
6
9
10
3
4
10
Note: In CScD-327 this is an example of finding the longest simple path, but the algorithm used
requires that edges have non-zero values (since edges in use are turned negative). Consequently the data
file for this example has used edges of weight 1 for the “dummy” edges (5,8) and (6,8).
Listing of All Simple Paths:
Printed 2020/12/2 at 20:56
