MODEL 5: FINDING THE OPTIMAL ROUTES USING DIJKSTRA’S ALGORITHMYohahn Jo

Class of 2011

Systems Engineering

DIJKSTRA’S ALGORITHM

Solves the single-source shortest-path problems Should have nonnegative weight

• “Single-source shortest path problem is the problem of finding a path between two vertices such that sum of its weights of its constituent edges is minimized”

MODEL 5• Maximize phone calls from Jonesville to Smithsboro• Optimal Routing• Assume that calls do not overlap

A: Jonesville

A: Jonesville

B: Greenst

own

B: Greenst

own

C: Smithfiel

d

C: Smithfiel

d

D: Jonesburg

h

D: Jonesburg

h

E:Greenford

E:Greenford

F: Smithsbor

o

F: Smithsbor

o3

5

8

4

6

3

2

5

9

8

OPTIMAL ROUTING

F A B C D E F 0 0 0 9F 8F D 0 13D 12D 9F 14D E 28C 23C 20E 9F 14D C 28B 23C 20E 9F 14D

AA

BB

CC

DD

EE

FF3

5

8

4

6

3

2

5

9

8

OPTIMAL ROUTING CONTINUED

Our optimal route is ABCEDF or ACEDF

AA

B:B:

CC

DD

EE

FF3

5

8

4

6

3

25

9

8

MAXIMUM NUMBER OF CALLS

Split into two cases, then eliminate

AA

BB

CC

DD

EE

FF3

5

4

6

3

25

9

8

AA

B:B:

CC

DD

EE

FF3

8

4

6

3

25

9

8

8 + 6+ 5+ 5 +1 + 2 + 2 = 29 5+ 3+ 3+ 3+ 3 + 2 + 2 + 2 = 23 Total 52

AA

BB

CC

DD

EE

FF3

8

4

63

25

9

8

AA

BB

CC

DD

EE

FF30

54

63

25

9

8

QUESTIONS?

WORKS CITED

http://www.youtube.com/watch?v=8Ls1RqHCOPw

http://brpreiss.com/books/opus4/html/page566.html#SECTION0017411000000000000000