Practice Prelim 2 Solutions

Practice Prelim 2 Solutions - ORIE 3310/5310 Practice...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
ORIE 3310/5310 Practice Prelim 2 (Spr2009) Solutions Spring 2010 1. (a) See class notes on Bellman’s algorithm (for finding a shortest (1 , n )-path in a directed acyclic graph). (b) Now suppose we wish to find a shortest (1 , n )-path which contains a specific edge , say edge ( i, j ). How would you use the basic procedure to achieve this? Solution. There are two ways to solve this problem. The first method: Find the shortest path from 1 to i using the basic procedure (Bellman), then find the shortest path from j to n . Then, the two solutions together with edge ( i, j ) is a shortest path from 1 to n that contains edge ( i, j ). Note that it is possible that there is no solution to one of these problems (i.e. no path from 1 to i or no path from j to n ), in which case we know that there is no path from 1 to n that contains ( i, j ). The second method: change the length of edge ( i, j ) to c ij - M , where M is a sufficiently large positive number (for example, you could choose M to be the sum of the absolute value of all other edge costs). Then, since we wish to minimize total path length, the
Image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern