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Shortest Path from G to C Using Dijkstra’s Algorithm. Hamid Behravan. 2. B. C. 1. 3. 2. 6. 3. 4. 4. D. E. F. A. 1. 5. 2. 5. G. H. 5. Unsolved Node. Solved Node. We will be finding the shortest path from origin, G, to the destination, C, using Dijkstra’s Algorithm.

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slide1

Shortest Path from G to C Using Dijkstra’s Algorithm

HamidBehravan

2

B

C

1

3

2

6

3

4

4

D

E

F

A

1

5

2

5

G

H

5

Unsolved Node

Solved Node

We will be finding the shortest path from origin, G, to the destination, C, using Dijkstra’s Algorithm.

slide2

Shortest Path from G to C Using Dijkstra’s Algorithm

2

B

C

1

3

2

6

3

4

4

D

E

F

A

1

5

2

5

G

H

5

Unsolved Node

Solved Node

Initialize by displaying the origin as solved node. We labeled it as 0, since it has 0 units from the origin.

slide3

Shortest Path from G to C Using Dijkstra’s Algorithm

2

B

C

1

3

2

6

3

4

4

D

E

F

A

1

5

2

5

G

H

5

0

Unsolved Node

Solved Node

Initialize by displaying the origin as solved node. We labeled it as 0, since it has 0 units from the origin.

slide4

Shortest Path from G to C Using Dijkstra’s Algorithm

2

B

C

1

3

2

6

3

4

4

D

E

F

A

1

5

2

5

G

H

5

0

Unsolved Node

Solved Node

Identify all unsolved node connected to any solved node.

slide5

Shortest Path from G to C Using Dijkstra’s Algorithm

2

B

C

1

3

2

6

3

4

4

D

E

F

A

1

5

2

5

G

H

5

0

Unsolved Node

Solved Node

Identify all unsolved node connected to any solved node.

slide6

Shortest Path from G to C Using Dijkstra’s Algorithm

2

B

C

1

3

2

6

3

4

4

D

E

F

A

1

5

2

5

G

H

5

0

Unsolved Node

Solved Node

For each node connecting a solved and unsolved nodes, calculate the candidate distance.

Candidate Distance = Distance to the solved node + Length of arc

slide7

Shortest Path from G to C Using Dijkstra’s Algorithm

2

B

C

1

3

2

6

3

5

4

4

D

E

F

A

2

2

5

0+5

1

5

0+2

5

G

H

0+5

0

5

Unsolved Node

Solved Node

For each node connecting a solved and unsolved nodes, calculate the candidate distance.

Candidate Distance = Distance to the solved node + Length of arc

slide8

Shortest Path from G to C Using Dijkstra’s Algorithm

2

B

C

1

3

2

6

3

5

4

4

D

E

F

A

2

2

5

0+5

1

5

0+2

5

G

H

0+5

0

5

Unsolved Node

Solved Node

Choose the smallest Node Distance

slide9

Shortest Path from G to C Using Dijkstra’s Algorithm

2

B

C

1

3

2

6

3

5

4

4

D

E

F

A

2

2

5

1

5

5

G

H

0

Unsolved Node

Solved Node

Change Node A to solved and labeled it with the candidate distance.

slide10

Shortest Path from G to C Using Dijkstra’s Algorithm

2

B

C

1

3

2

6

3

4

4

D

E

F

A

2

5

1

5

2

G

H

0

5

Unsolved Node

Solved Node

Add the arc to arc set

Repeat all these steps until we get to destination node

slide11

Shortest Path from G to C Using Dijkstra’s Algorithm

3

2

B

C

1+2=3

3

1

2

6

5

5

3+2=5

4

4

D

E

F

A

2

3

5

0+5=5

1

5

2

5

G

H

0+5=5

0

5

Unsolved Node

Solved Node

Calculate the candidate distance of each connecting arc.

slide12

Shortest Path from G to C Using Dijkstra’s Algorithm

3

2

B

C

1+2=3

3

1

2

6

4

4

D

E

F

A

2

3

5

1

5

2

5

G

H

0

Unsolved Node

Solved Node

Choose the smallest Node Distance

slide13

Shortest Path from G to C Using Dijkstra’s Algorithm

3

2

B

C

3

1

2

6

4

4

D

E

F

A

2

3

5

1

5

2

5

G

H

0

5

Unsolved Node

Solved Node

Change Node B to solved and labeled it with the candidate distance. Add the arc to the arc set.

slide14

Shortest Path from G to C Using Dijkstra’s Algorithm

3

2

B

C

3

1

2

6

4

4

D

E

F

A

2

3

5

1

5

2

5

G

H

0

5

Unsolved Node

Solved Node

We have not reached our destination node, so we will continue.

slide15

Shortest Path from G to C Using Dijkstra’s Algorithm

3

2

B

C

3

1

2

6

4

4

D

E

F

A

2

3

5

1

5

2

5

G

H

0

5

Unsolved Node

Solved Node

Identify all unsolved node connected to any solved node. Calculate the candidate distance of each connecting arc.

slide16

Shortest Path from G to C Using Dijkstra’s Algorithm

3

5

3+2=5

B

C

2

3

1

2

6

3+2=5

0+5=5

5

4

4

D

E

F

A

2

3

5

1

5

0+5=5

2

5

G

H

5

0+5=5

0

5

Unsolved Node

Solved Node

Identify all unsolved node connected to any solved node. Calculate the candidate distance of each connecting arc.

slide17

Shortest Path from G to C Using Dijkstra’s Algorithm

3

5

3+2=5

B

C

2

3

1

2

6

3+2=5

0+5=5

5

4

4

D

E

F

A

2

3

5

1

5

0+5=5

2

5

G

H

5

0+5=5

0

5

Unsolved Node

Solved Node

We have a tie for the smallest candidate distance. If we choose C, then we get to our destination.

slide18

Shortest Path from G to C Using Dijkstra’s Algorithm

3

5

2

B

C

3

1

2

6

4

4

D

E

F

A

2

3

5

1

5

2

5

G

H

0

Unsolved Node

Solved Node

The Shortest Root to C is:

slide19

Shortest Path from G to C Using Dijkstra’s Algorithm

3

5

2

B

C

3

1

2

6

4

4

D

E

F

A

2

3

5

1

5

2

5

G

H

0

Unsolved Node

Solved Node

The Shortest Root to C is:

G – A – B - C