20_Shortest_path.pptx

# Example with the first pass k 1 we attempt passing

• 148

This preview shows pages 95–109. Sign up to view the full content.

Example With the first pass, k = 1 , we attempt passing through vertex v 1 0 0.100 0.101 0.142 0.277 0.465 0 0.191 0.192 0.587 0.245 0.554 0 0.333 0.931 1.032 0.668 0.656 0 0.151 0.867 0.119 0.352 0.398 0

This preview has intentionally blurred sections. Sign up to view the full version.

Example With the first pass, k = 1 , we attempt passing through vertex v 1 We would start: (2, 3) (2, 1, 3) 0.191 0.465 + 0.101 0 0.100 0.101 0.142 0.277 0.465 0 0.191 0.192 0.587 0.245 0.554 0 0.333 0.931 1.032 0.668 0.656 0 0.151 0.867 0.119 0.352 0.398 0
Example With the first pass, k = 1 , we attempt passing through vertex v 1 We would start: (2, 4) (2, 1, 4) 0.192 0.465 + 0.142 0 0.100 0.101 0.142 0.277 0.465 0 0.191 0.192 0.587 0.245 0.554 0 0.333 0.931 1.032 0.668 0.656 0 0.151 0.867 0.119 0.352 0.398 0

This preview has intentionally blurred sections. Sign up to view the full version.

Example With the first pass, k = 1 , we attempt passing through vertex v 1 We would start: (2, 5) (2, 1, 5) 0.587 0.465 + 0.277 0 0.100 0.101 0.142 0.277 0.465 0 0.191 0.192 0.587 0.245 0.554 0 0.333 0.931 1.032 0.668 0.656 0 0.151 0.867 0.119 0.352 0.398 0
Example With the first pass, k = 1 , we attempt passing through vertex v 1 Here is a shorter path: (3, 2) (3, 1, 2) 0.554 > 0.245 + 0.100 = 0.345 0 0.100 0.101 0.142 0.277 0.465 0 0.191 0.192 0.587 0.245 0.554 0 0.333 0.931 1.032 0.668 0.656 0 0.151 0.867 0.119 0.352 0.398 0

This preview has intentionally blurred sections. Sign up to view the full version.

Example With the first pass, k = 1 , we attempt passing through vertex v 1 We update the table (3, 2) (3, 1, 2) 0.554 > 0.245 + 0.100 = 0.345 0 0.100 0.101 0.142 0.277 0.465 0 0.191 0.192 0.587 0.245 0.345 0 0.333 0.931 1.032 0.668 0.656 0 0.151 0.867 0.119 0.352 0.398 0
Example With the first pass, k = 1 , we attempt passing through vertex v 1 And a second shorter path: (3, 5) (3, 1, 5) 0.931 > 0.245 + 0.277 = 0.522 0 0.100 0.101 0.142 0.277 0.465 0 0.191 0.192 0.587 0.245 0.345 0 0.333 0.931 1.032 0.668 0.656 0 0.151 0.867 0.119 0.352 0.398 0

This preview has intentionally blurred sections. Sign up to view the full version.

Example With the first pass, k = 1 , we attempt passing through vertex v 1 We update the table 0 0.100 0.101 0.142 0.277 0.465 0 0.191 0.192 0.587 0.245 0.345 0 0.333 0.522 1.032 0.668 0.656 0 0.151 0.867 0.119 0.352 0.398 0
Example With the first pass, k = 1 , we attempt passing through vertex v 1 Continuing… We find that no other shorter paths through vertex v 1 exist 0 0.100 0.101 0.142 0.277 0.465 0 0.191 0.192 0.587 0.245 0.345 0 0.333 0.522 1.032 0.668 0.656 0 0.151 0.867 0.119 0.352 0.398 0

This preview has intentionally blurred sections. Sign up to view the full version.

Example With the next pass, k = 2 , we attempt passing through vertex v 2 There are three shorter paths: (5, 1) (5, 2, 1) 0.867 > 0.119 + 0.465 = 0.584 (5, 3) (5, 2, 3) 0.352 > 0.119 + 0.191 = 0.310 (5, 4) (5, 2, 4) 0.398 > 0.119 + 0.192 = 0.311 0 0.100 0.101 0.142 0.277 0.465 0 0.191 0.192 0.587 0.245 0.345 0 0.333 0.522 1.032 0.668 0.656 0 0.151 0.867 0.119 0.352 0.398 0
Example With the next pass, k = 2 , we attempt passing through vertex v 2 We update the table 0 0.100 0.101 0.142 0.277 0.465 0 0.191 0.192 0.587 0.245 0.345 0 0.333 0.522 1.032 0.668 0.656 0 0.151 0.584 0.119 0.310 0.311 0

This preview has intentionally blurred sections. Sign up to view the full version.

Example With the next pass, k = 3 , we attempt passing through vertex v 3 There are three shorter paths: (2, 1) (2, 3, 1) 0.465 > 0.191 + 0.245 = 0.436 (4, 1) (4, 3, 1) 1.032 > 0.656 + 0.245 = 0.901 (5, 1) (5, 3, 1) 0.584 > 0.310 + 0.245 = 0.555 0 0.100 0.101 0.142 0.277 0.465 0 0.191 0.192 0.587 0.245 0.345 0 0.333 0.522 1.032 0.668 0.656 0 0.151 0.584 0.119 0.310 0.311 0
Example With the next pass, k = 3 , we attempt passing through vertex v 3 We update the table 0 0.100 0.101 0.142 0.277 0.436 0 0.191 0.192 0.587 0.245 0.345 0 0.333 0.522 0.901 0.668 0.656 0 0.151 0.555 0.119 0.310 0.311 0

This preview has intentionally blurred sections. Sign up to view the full version.

Example With the next pass, k = 4 , we attempt passing through vertex v 4 There are two shorter paths: (2, 5) (2, 4, 5) 0.587 > 0.192 + 0.151 (3, 5) (3, 4, 5) 0.522 > 0.333 + 0.151 0 0.100 0.101 0.142 0.277 0.436 0 0.191 0.192 0.587 0.245 0.345 0 0.333 0.522 0.901 0.668
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern