the critical-path algorithm - hampden-sydney...

The Critical-Path AlgorithmLecture 37

Sections 8.5

Robb T. Koether

Hampden-Sydney College

Mon, Nov 27, 2017

Robb T. Koether (Hampden-Sydney College) The Critical-Path Algorithm Mon, Nov 27, 2017 1 / 15

1 The Critical-Path Algorithm

2 Example

3 Assignment


Outline


2 Example

3 Assignment


The Critical-Path Algorithm

Definition (The Critical-Path Algorithm)The critical-path algorithm creates a schedule by the following method.

1 Use the backflow algorithm to find the critical time of every task inthe project.

2 Create a priority list with the tasks listed in order of decreasingcritical time.

3 Use that priority list to create a schedule.


The Backflow Algorithm

Example (The Backflow Algorithm)

Start(0)B(5)

D(2)

A(6)

C(7)

End(0)

E(5) H(4)

G(3)

F(3)




Start(0)B(5)

D(2)

A(6)

C(7)

End(0)

E(5) H(4)[4]

G(3)[3]

F(3)[3]




Start(0)B(5)

D(2)[5]

A(6)

C(7)

End(0)

E(5)[9] H(4)[4]

G(3)[3]

F(3)[3]




Start(0)[16]B(5)[14]

D(2)[5]

A(6)[11]

C(7)[16]

End(0)

E(5)[9] H(4)[4]

G(3)[3]

F(3)[3]


Example

Example (The Critical-Path Algorithm)

Start(16)B(14)

D(5)

A(11)

C(16)

End(0)

E(9) H(4)

G(3)

F(3)

The priority list is C,B,A,E ,D,H,F ,G.


Example


Start(0)[16]B(5)[14]

D(2)[5]

A(6)[11]

C(7)[16]

End(0)

E(5)[9] H(4)[4]

G(3)[3]

F(3)[3]

Priority list: C,B,A,E ,D,H,F ,G

0 5 10 15 20

Processor 1Processor 2


Example


Start(0)[16]B(5)[14]

D(2)[5]

A(6)[11]

C(7)[16]

End(0)

E(5)[9] H(4)[4]

G(3)[3]

F(3)[3]


C(7)

0 5 10 15 20

Processor 1Processor 2


Example


Start(0)[16]B(5)[14]

D(2)[5]

A(6)[11]

C(7)[16]

End(0)

E(5)[9] H(4)[4]

G(3)[3]

F(3)[3]


C(7)

0 5 10 15 20

B(5)Processor 1Processor 2


Example


Start(0)[16]B(5)[14]

D(2)[5]

A(6)[11]

C(7)[16]

End(0)

E(5)[9] H(4)[4]

G(3)[3]

F(3)[3]


C(7)

0 5 10 15 20

B(5) A(6)Processor 1Processor 2


Example


Start(0)[16]B(5)[14]

D(2)[5]

A(6)[11]

C(7)[16]

End(0)

E(5)[9] H(4)[4]

G(3)[3]

F(3)[3]


C(7)

0 5 10 15 20

B(5) A(6)E(5)Processor 1

Processor 2


Example


Start(0)[16]B(5)[14]

D(2)[5]

A(6)[11]

C(7)[16]

End(0)

E(5)[9] H(4)[4]

G(3)[3]

F(3)[3]


C(7)

0 5 10 15 20

B(5) A(6)E(5)

D(2)Processor 1Processor 2


Example


Start(0)[16]B(5)[14]

D(2)[5]

A(6)[11]

C(7)[16]

End(0)

E(5)[9] H(4)[4]

G(3)[3]

F(3)[3]


C(7)

0 5 10 15 20

B(5) A(6)E(5)

D(2)H(4)Processor 1

Processor 2


Example


Start(0)[16]B(5)[14]

D(2)[5]

A(6)[11]

C(7)[16]

End(0)

E(5)[9] H(4)[4]

G(3)[3]

F(3)[3]


C(7)

0 5 10 15 20

B(5) A(6)E(5)

D(2)H(4)

F(3)Processor 1Processor 2


Example


Start(0)[16]B(5)[14]

D(2)[5]

A(6)[11]

C(7)[16]

End(0)

E(5)[9] H(4)[4]

G(3)[3]

F(3)[3]


C(7)

0 5 10 15 20

B(5) A(6)E(5)

D(2)H(4)

F(3)Processor 1Processor 2

G(3)


Outline


2 Example

3 Assignment


Example (Exercise 55)

Precedent ProcessingTask Tasks Time

A 10B 5C B 4D C,G 1E D 8F 3G H 7H F 1J H 6



Start(0)B(5) D(1)

A(10)

C(4)End(0)

E(8)

H(1)

G(7)

F(3) J(6)

Schedule the tasks using 2 processors.



Precedent Processing CriticalTask Tasks Time Time

A 10

10

B 5

18

C B 4

13

D C,G 1

9

E D 8

8

F 3

20

G H 7

16

H F 1

17

J H 6

6




A 10 10B 5

18

C B 4

13

D C,G 1

9

E D 8

8

F 3

20

G H 7

16

H F 1

17

J H 6

6




A 10 10B 5

18

C B 4

13

D C,G 1

9

E D 8 8F 3

20

G H 7

16

H F 1

17

J H 6

6




A 10 10B 5

18

C B 4

13

D C,G 1

9

E D 8 8F 3

20

G H 7

16

H F 1

17

J H 6 6




A 10 10B 5

18

C B 4

13

D C,G 1 9E D 8 8F 3

20

G H 7

16

H F 1

17

J H 6 6




A 10 10B 5

18

C B 4 13D C,G 1 9E D 8 8F 3

20

G H 7

16

H F 1

17

J H 6 6




A 10 10B 5

18

C B 4 13D C,G 1 9E D 8 8F 3

20

G H 7 16H F 1

17

J H 6 6




A 10 10B 5

18

C B 4 13D C,G 1 9E D 8 8F 3

20

G H 7 16H F 1 17J H 6 6




A 10 10B 5 18C B 4 13D C,G 1 9E D 8 8F 3

20

G H 7 16H F 1 17J H 6 6




A 10 10B 5 18C B 4 13D C,G 1 9E D 8 8F 3 20G H 7 16H F 1 17J H 6 6



Start(0)[20]B(5)[18] D(1)[9]

A(10)[10]

C(4)[13]End(0)

E(8)[8]

H(1)[17]

G(7)[16]

F(3)[20] J(6)[6]



Example

A(5)

B(8)

E(9)

D(2)

F(7)

G(4)

C(5)

I(3)

H(8)

END(0)START(0)

J(6)



Example

A(5)

B(8)

E(9)

D(2)

F(7)

G(4)

C(5)

I(3)

H(8)

END(0)START(0)

J(6)

Compare to the Decreasing-Time Method.


Outline


2 Example

3 Assignment


Assignment

AssignmentChapter 8: Exercises 49, 50, 51, 52, 56.


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