M ODEL 5: F INDING THE O PTIMAL R OUTES USING D IJKSTRA ’ S A LGORITHM Yohahn Jo Class of 2011...
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Transcript of M ODEL 5: F INDING THE O PTIMAL R OUTES USING D IJKSTRA ’ S A LGORITHM Yohahn Jo Class of 2011...
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MODEL 5: FINDING THE OPTIMAL ROUTES USING DIJKSTRA’S ALGORITHMYohahn Jo
Class of 2011
Systems Engineering
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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”
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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
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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
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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
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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
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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
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QUESTIONS?
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WORKS CITED
http://www.youtube.com/watch?v=8Ls1RqHCOPw
http://brpreiss.com/books/opus4/html/page566.html#SECTION0017411000000000000000