dijkstra's algorithm ppg

7/29/2019 Dijkstra's Algorithm Ppg

1/12

by

MDM KHARSHIAH KHALID


2/12

Edsger Wybe Dijkstra (pronounced

Deekstrah) (1930-2002)

b. Rotterdam, Netherlands; worked

in Amsterdam and also Texas,USA

Edsger Dijkstra studied TheoreticalPhysics at the University of Leidenbeforemoving into the field of ComputerScience. He worked for the

MathematischCentrum in Amsterdam and then theBurroughs Corporation, which hadprogressedfrom making adding machines to

typewriters and computers. He laterheld theSchlumberger Centennial Chair inComputer Sciences at the Universityof Texas.


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Edsger Wybe Dijkstra (pronounced

Deekstrah) (1930-2002)

b. Rotterdam, Netherlands; worked

in Amsterdam and also Texas, USA

In Graph Theory, he is known best for

Dijkstras Algorithm for finding theShortest Path between two points in anetwork, which he developed in 1959.This is alabelling procedure which identifies thesmallest total path length to each vertex

fromthe starting point. Tracing back from thefinish vertex finds the shortest path itself.It is an example of a greedy algorithmbecause of the step during each iterationwherethe vertex with the lowest working valueis chosen as the best and is thenpermanentlylabelled.


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Order of

labelling

Label (i.e

Permanentlabel)

Working

values


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1 0

S

A

B

T

D

C

3

11

58

6

41

2

4

Step 1

Label start node S

with permanent label

(P-label) of 0.4


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4

3

1 0

6

S

A

B

T

D

C

3

11

58

6

41

2

4

Step 2

For all nodes that

can be reached

directly from S,

assign temporary

labels (T-labels)

equal to their direct

distance from S

4


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4

2 3

1 0

6

S

A

B

T

D

C

3

11

58

6

41

2

4

Step 3

Select the node with

smallest T label and

makes its label

permanent. In this

case the node is A.

The P-label

represents the

shortest distancefrom S to that node.

Put the order of

labeling as 2.


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4

2 3

1 0

6

S

A

B

T

D

C

3

11

58

6

41

2

4

Step 4

Consider all nodes

that can be reached

from A, that are B

and T. Shortestroute from S to B via

A is 3+4 =7, but B is

already labelled as 6

and its the best sofar. The shortest

route from S to T via

A is 3 + 11 = 14. Put

T-label as 14 in T

4

14


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3 4

2 3

1 0

6

S

A

B

T

D

C

3

11

58

6

41

2

4

Step 5

Compare node T,

B and C. The

smallest T label is

now 4 at C. Sincethis value cannot

be improved, it

becomes P-label

of 4. Put the orderof labeling at C as

3

4

14


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3 4

2 3

1 0

4 5

S

A

B

T

D

C

3

11

58

6

41

2

4

Step 6

Consider all nodes that

can be reached from C,

that are B and D.

Shortest route from S to B

via C is 4+1 =5 which is

shorter than 6. Change Tlabel 6 to P label 5. The

shortest route from S to D

via C is 4 + 4 = 8. Put T-

label as 8 in D. Compare

B and D. B is less than D,so the next node is B. Put

the order of labeling at B

as 4

4

14

8


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3 4

4

2 3

3

1 0

4 5

6,5S

A

B

T

D

C

3

11

58

6

41

2

4

Step 7

Consider all nodes thatcan be reached from B;

that are D and T.

Shortest route from S to

D via B is 5+2 =7 which

is shorter than 8. ChangeT label 8 to P label 7. The

shortest route from S to T

via B is 5 + 8 = 13. This is

smaller than 14 so

change to 13 in T as Tlabel. Compare T and D.

D is less than T so chose

D as the next node. Put

the order of labeling as 5

in D

4

6 13

14,13

5 7

8,7


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3 4

4

2 3

3

1 0

4 5

6,5S

A

B

T

D

C

3

11

58

6

41

2

4

Step 8

The last node is T. Put theorder of labeling as 6 in T.

Compare the routes from

S to T via A (3 + 11 =14),

via B ( 5 + 8 =13) and via

D (7 + 5 =12). It seemsthat the shortest route

from S to T is via D.

Change the T label in T

(13) to P label with the

value 12. Therefore theshortest way from S to T

is SCBDT which is 12

4

6 12

14,13,12

5 7

8,7

dijkstra's algorithm ppg

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