Discrete Math Mr' Gilbert

1
Discrete MathMr. Gilbert

• Graphs and Their Applications
• 4.2 Critical Paths

2
Essential Skills
1. Students will distinguish between the uses of
Euler and Hamiltonian circuits. 2. Students will
use Kruskals Algorithm to find a minimum cost
spanning tree. 3. Students will find the optimal
solution to a traveling salesperson problem.  
3
Essential Questions

• What is the relationship between graphs and
  matrices?
• What are Euler and Hamiltonian paths and how do
  they apply in the real world.
• Why does no map require five colors?

4
Students shall be able to

• Read and understand project graphs and the
  critical path.

• Find a projects critical path.

5
Agenda

• Warm up
• Homework review
• Lesson or activity
• Class work
• Summary

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Communicate Effectively

• PERT The Program Evaluation and Review Technique
  developed by the Navy to estimate large projects.
  
• Critical Path The longest direct path through
  the project.
• Example of the critical path Start ABDE Finish

B
3
4
Finish
A
Start
1
D
E
1
1
C
7
Communicate with Equations(Extra Credit or A
work)

• PERT FORMULA Is useful in finding the estimated
  time for large projects it uses three estimates
  the optimistic (a), most likely (m) and
  pessimistic (b).

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Communicate Effectively

• Day 0 By convention the beginning of a project,
  before any schedule is known.
• Earliest Start Date (EST) The earliest a task
  can begin, if all preceding tasks are complete.
• Latest Start Date (LST) The latest a task can
  begin without changing the critical path.

9
Recall the Yearbook Project
D
C
3
F
2
1
2
2
1
3
0
Start
Finish
1
A
H
B
5
1
G
1
E
10
Yearbook Project with EST
(5) D
(2)C
3
(7)F
2
1
2
2
1
3
0
Start
Finish
1
A (1)
B (1)
H (12)
(15)
5
1
G (7)
1
E (2)
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Yearbook Project with Critical Path
(5) D
(2)C
3
(7)F
2
1
2
2
3
1
0
Start
Finish
1
B (1)
A (1)
H (12)
(15)
5
1
G (7)
1
E (2)
Critical Path start-ABCDGH-finish